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mathematics
calculus 10th edition

Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions

In Exercises use the divergence test given in Exercise 31 to show that the series diverges.Data from in Exercise 31Use the Limit Comparison Test with the harmonic series to show that the series Σ an (where 0 < an < an-1) diverges when is finite and nonzero. n=1 n3 5n4 +3
In Exercises use Theorem 9.11 to determine the convergence or divergence of the p-series.Data from in Theorem 9.11 THEOREM 9.11 Convergence of p-Series The p-series n=1 1 1 1 = + + nP 1P 2P 1 3P + 1 4P converges for p > 1, and diverges for 0 < p ≤ 1.
In Exercises(a) Write the repeating decimal as a geometric series(b) Write its sum as the ratio of two integers.0.81̅
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an 5n 3″
In Exercises use Theorem 9.15 to determine the number of terms required to approximate the sum of the series with an error of less than 0.001.Data from in Theorem 9.15 THEOREM 9.15 Alternating Series Remainder If a convergent alternating series satisfies the condition an+1 ≤ a, then the absolute
In Exercises use the polynomial test given in Exercise 32 to determine whether the series converges or diverges.Data from in Exercise 32Prove that, if P(n) and Q(n) are polynomials of degree j and k, respectively, then the seriesconverges if j < k - 1 and diverges if j ≥ k - 1.
In Exercises(a) Write the repeating decimal as a geometric series(b) Write its sum as the ratio of two integers.0.36̅
In Exercises use Theorem 9.15 to determine the number of terms required to approximate the sum of the series with an error of less than 0.001.Data from in Theorem 9.15 THEOREM 9.15 Alternating Series Remainder If a convergent alternating series satisfies the condition an+1 ≤ a, then the absolute
In Exercises use Theorem 9.11 to determine the convergence or divergence of the p-series.Data from in Theorem 9.11 THEOREM 9.11 Convergence of p-Series The p-series n=1 1 1 1 = + + nP 1P 2P 1 3P + 1 4P converges for p > 1, and diverges for 0 < p ≤ 1.
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an || In(n³) 2n
In Exercises use the polynomial test given in Exercise 32 to determine whether the series converges or diverges.Data from in Exercise 32Prove that, if P(n) and Q(n) are polynomials of degree j and k, respectively, then the seriesconverges if j < k - 1 and diverges if j ≥ k - 1. n=1 1 n³
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an /n 3√/n + 1
In Exercises use Theorem 9.11 to determine the convergence or divergence of the p-series.Data from in Theorem 9.11 THEOREM 9.11 Convergence of p-Series The p-series n=1 1 1 1 = + + nP 1P 2P 1 3P + 1 4P converges for p > 1, and diverges for 0 < p ≤ 1.
In Exercises use the polynomial test given in Exercise 32 to determine whether the series converges or diverges.Data from in Exercise 32Prove that, if P(n) and Q(n) are polynomials of degree j and k, respectively, then the seriesconverges if j < k - 1 and diverges if j ≥ k - 1. 13 + - +
In Exercises use Theorem 9.11 to determine the convergence or divergence of the p-series.Data from in Theorem 9.11 THEOREM 9.11 Convergence of p-Series The p-series n=1 1 1 1 = + + nP 1P 2P 1 3P + 1 4P converges for p > 1, and diverges for 0 < p ≤ 1.
In Exercises(a) Write the repeating decimal as a geometric series(b) Write its sum as the ratio of two integers.0.4̅
In Exercises use Theorem 9.15 to determine the number of terms required to approximate the sum of the series with an error of less than 0.001.Data from in Theorem 9.15 THEOREM 9.15 Alternating Series Remainder If a convergent alternating series satisfies the condition an+1 ≤ a, then the absolute
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an 10n² + 3n+ 7 2n² - 6
In Exercises find the sum of the convergent series. n=1 1 9n² + 3n - 2
In Exercises use Theorem 9.15 to determine the number of terms required to approximate the sum of the series with an error of less than 0.001.Data from in Theorem 9.15 THEOREM 9.15 Alternating Series Remainder If a convergent alternating series satisfies the condition an+1 ≤ a, then the absolute
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an || 1 + (−1)n 2 n²
In Exercises use Theorem 9.15 to determine the number of terms required to approximate the sum of the series with an error of less than 0.001.Data from in Theorem 9.15 THEOREM 9.15 Alternating Series Remainder If a convergent alternating series satisfies the condition an+1 ≤ a, then the absolute
In Exercises find the sum of the convergent series. n=1 (sin 1)n
In Exercises use the polynomial test given in Exercise 32 to determine whether the series converges or diverges.Data from in Exercise 32Prove that, if P(n) and Q(n) are polynomials of degree j and k, respectively, then the seriesconverges if j < k - 1 and diverges if j ≥ k - 1.
In Exercises use the Integral Test to determine the convergence or divergence of the p-series. 18 n=1 1 n¹/4
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an = (-1)" n n+ 1,
In Exercises find the sum of the convergent series. Σ [(0.3) + (0.8)"] n=0
Prove that, if P(n) and Q(n) are polynomials of degree j and k, respectively, then the seriesconverges if j < k - 1 and diverges if j ≥ k - 1. n=1 P(n) Q(n)
In Exercises use Theorem 9.15 to determine the number of terms required to approximate the sum of the series with an error of less than 0.001.Data from in Theorem 9.15 n=1 (−1)n +1 那
In Exercises test for convergence or divergence, using each test at least once. Identify which test was used.(a) nth-Term Test (b) Geometric Series Test(c) p-Series Test (d) Telescoping Series Test(e) Integral Test (f ) Direct Comparison Test(g) Limit Comparison Test n=1 3 n(n + 3)
In Exercises find the sum of the convergent series. n=0 1 1 2n 3n 1
Use the Limit Comparison Test with the harmonic series to show that the series Σ an (where 0 < an < an-1) diverges when is finite and nonzero. lim na 81x n- n
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. טי 5 = 8+. ן n
In Exercises use the Integral Test to determine the convergence or divergence of the p-series. 18 n=1 n 1 1/2
In Exercises find the sum of the convergent series. 9 − 3 + 1 − 3 + ··
In Exercises test for convergence or divergence, using each test at least once. Identify which test was used.(a) nth-Term Test (b) Geometric Series Test(c) p-Series Test (d) Telescoping Series Test(e) Integral Test (f ) Direct Comparison Test(g) Limit Comparison Test n Σ (n² +
In Exercises approximate the sum of the series by using the first six terms. n=1 (−1)n+1 n 3n
In Exercises approximate the sum of the series by using the first six terms. n=1 (-1)+12 n³
In Exercises find the sum of the convergent series. 8 + 6 + 2/2 + 2²/7/7 +
In Exercises use the Integral Test to determine the convergence or divergence of the p-series. n=1 -| 1 n³ 3
In Exercises test for convergence or divergence, using each test at least once. Identify which test was used.(a) nth-Term Test (b) Geometric Series Test(c) p-Series Test (d) Telescoping Series Test(e) Integral Test (f ) Direct Comparison Test(g) Limit Comparison Test n=1 1 \n +
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an || 5 n+ 2
In Exercises explain why the Integral Test does not apply to the series. n=1 sin n2 n
In Exercises find the sum of the convergent series. n=1 1 (2n + 1)(2n + 3)
In Exercises use a graphing utility to graph the first 10 terms of the sequence. Use the graph to make an inference about the convergence or divergence of the sequence. Verify your inference analytically and, if the sequence converges, find its limit. a₁ = 2 an 1 4n
In Exercises approximate the sum of the series by using the first six terms. n=1 (-1)^²+14 In(n + 1)
In Exercises approximate the sum of the series by using the first six terms. n=0 (-1)^5 n!
In Exercises test for convergence or divergence, using each test at least once. Identify which test was used.(a) nth-Term Test (b) Geometric Series Test(c) p-Series Test (d) Telescoping Series Test(e) Integral Test (f ) Direct Comparison Test(g) Limit Comparison Test n=1 2n 3n - 2
In Exercises find the sum of the convergent series. n=1 4 n(n + 2)
In Exercises explain why the Integral Test does not apply to the series. n=1 2 + sin n n
In Exercises use a graphing utility to graph the first 10 terms of the sequence. Use the graph to make an inference about the convergence or divergence of the sequence. Verify your inference analytically and, if the sequence converges, find its limit. an sin NTT 2
In Exercises find the sum of the convergent series. n=0 5 n
In Exercises test for convergence or divergence, using each test at least once. Identify which test was used.(a) nth-Term Test (b) Geometric Series Test(c) p-Series Test (d) Telescoping Series Test(e) Integral Test (f ) Direct Comparison Test(g) Limit Comparison Test n=2 1 n³ - 8
In Exercises explain why the Integral Test does not apply to the series. n=1 en cos n
In Exercises use a graphing utility to graph the first 10 terms of the sequence. Use the graph to make an inference about the convergence or divergence of the sequence. Verify your inference analytically and, if the sequence converges, find its limit. an 1 n3/2
In Exercises use a graphing utility to graph the first 10 terms of the sequence. Use the graph to make an inference about the convergence or divergence of the sequence. Verify your inference analytically and, if the sequence converges, find its limit. an 4n+ 1 n
In Exercises test for convergence or divergence, using each test at least once. Identify which test was used.(a) nth-Term Test (b) Geometric Series Test(c) p-Series Test (d) Telescoping Series Test(e) Integral Test (f ) Direct Comparison Test(g) Limit Comparison Test n=0 5 4 3 n
In Exercises find the sum of the convergent series. n=0 5 2/3 n
In Exercises determine the convergence or divergence of the series. n=1 2(−1)n+1 en e-n - n=1 (-1)n +¹ csch n
In Exercises(a) Find the sum of the series(b) Use a graphing utility to find the indicated partial sum Sn and complete the table(c) Use a graphing utility to graph the first 10 terms of the sequence of partial sums and a horizontal line representing the sum(d) Explain the relationship between the
In Exercises use the Integral Test to determine the convergence or divergence of the series, where is a positive integer. 18 n=1 nke-n
In Exercises find the limit (if possible) of the sequence. an = COS 2 n
In Exercises determine the convergence or divergence of the series. Σ (-1)+1. n=1 1.3.5. 1.4.7 · (2η – 1) (3n - 2)
In Exercises use the Integral Test to determine the convergence or divergence of the series, where is a positive integer. n=1 nk-1 nk + c
In Exercises(a) Find the sum of the series(b) Use a graphing utility to find the indicated partial sum Sn and complete the table(c) Use a graphing utility to graph the first 10 terms of the sequence of partial sums and a horizontal line representing the sum(d) Explain the relationship between the
In Exercises test for convergence or divergence, using each test at least once. Identify which test was used.(a) nth-Term Test (b) Geometric Series Test(c) p-Series Test (d) Telescoping Series Test(e) Integral Test (f ) Direct Comparison Test(g) Limit Comparison Test 18 n=1 3√/n n
In Exercises determine the convergence or divergence of the series. n=1 (-1)"+¹ n! 1.3.5 (2n - 1) .
In Exercises use the Limit Comparison Test to determine the convergence or divergence of the series. n=1 sin n
In Exercises find the limit (if possible) of the sequence. an 2n n² + 1
In Exercises(a) Find the sum of the series(b) Use a graphing utility to find the indicated partial sum Sn and complete the table(c) Use a graphing utility to graph the first 10 terms of the sequence of partial sums and a horizontal line representing the sum(d) Explain the relationship between the
In Exercises find the limit (if possible) of the sequence. an = 6+ 2 n²
In Exercises confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. n=1 n n² + 2n² + 1
In Exercises use the Limit Comparison Test to determine the convergence or divergence of the series. n=1 nk-1 nk + 1' k> 2
In Exercises determine the convergence or divergence of the series. n=1 (−1)n+1 √√n 3√/n
In Exercises determine the convergence or divergence of the series. n=1 u 1+u(I-) n+2 n
In Exercises confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. n=1 n n4+1 -
In Exercises confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. n=1 1 √n + 2
In Exercises use the Limit Comparison Test to determine the convergence or divergence of the series. n=1 n (n + 1)2n-1
In Exercises find the limit (if possible) of the sequence. an || 5n² n² + 2
In Exercises(a) Find the sum of the series(b) Use a graphing utility to find the indicated partial sum Sn and complete the table(c) Use a graphing utility to graph the first 10 terms of the sequence of partial sums and a horizontal line representing the sum(d) Explain the relationship between the
In Exercises verify that the infinite series converges. n=1 1 n(n + 2)
In Exercises simplify the ratio of factorials. (2n + 2)! (2n)!
In Exercises determine the convergence or divergence of the series. n=0 (−1)n (2n + 1)!
In Exercises confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. n=1 n+2 n+ 1 +1
In Exercises simplify the ratio of factorials. (2n − 1)! (2n + 1)!
In Exercises verify that the infinite series converges. n=1 1 n(n + 1)
In Exercises determine the convergence or divergence of the series. Ë n=0 (-1)" n!
In Exercises use the Limit Comparison Test to determine the convergence or divergence of the series. n=1 1 n²(n + 3)
In Exercises use the Limit Comparison Test to determine the convergence or divergence of the series. n=1 2n² - 1 3n5 + 2n + 1
In Exercises simplify the ratio of factorials. n! (n + 2)!
In Exercises verify that the infinite series converges. n=0 (-0.6)" = 1 - 0.6 + 0.36 – 0.216 + · -
In Exercises determine the convergence or divergence of the series. n=1 sin (2n-1) T п 2
In Exercises confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. n=1 1 (2n + 3)³
In Exercises simplify the ratio of factorials. (n + 1)! n!
In Exercises use the Limit Comparison Test to determine the convergence or divergence of the series. n=1 2+1 5 + 1
In Exercises verify that the infinite series converges. n=0 (0.9) = 1 +0.9 +0.81 +0.729 +
In Exercises confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. 1 n=2 n√Inn
In Exercises verify that the infinite series converges. 요. n=1 2 2,
In Exercises determine the convergence or divergence of the series. n=1 (-1)+¹ In(n + 1) n+ 1
Write the next two apparent terms of the sequence. Describe the pattern you used to find these terms. 6, -2, 0|N IN

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