1.)

Use the Direct Comparison Test to determine whether the series converges or diverges. 4 + 6 sinn an on- + 2 n= The comparison series is C where c = 1 and p = 2 which 7=1 TI= means an bn for all n > 1. by is a convergent p-series therefore M an converges v by the Direct Comparison Test. n=1 =1Use the Alternating Series Test to determine whether the series converges or diverges. (For limits, enter a number, "-infnity", "infinity", or "DNE" as appropriate.) 00 E(-1)m In(9n) 572 n=1 lim br 0 1-+00 O A. {by } is ultimately decreasing because the function f satifying f(n) = b,, is decreasing on the interval Therefore the series converges by the Alternating Series test. B. lim an = O , so the series diverges by the Divergence Test. 71-100Use the Alternating Series Test to determine whether the series converges or diverges. (For limits, enter a number, "-infnity", "infinity", or "DNE" as appropriate.) [(- 1)" ( 975 An* + 7 lim be = 0 n-+00 O A. {by } is ultimately decreasing because the function f satifying f(n) = b, is decreasing on the interval [2,infinity) Therefore the series converges by the Alternating Series test. OB. lim an = , so the series diverges by the Divergence Test.Use the Alternating Series Test to determine whether the series converges or diverges. (For limits, enter a number, "-infnity", "infinity", or "DNE" as appropriate.) DO (-1)-1 6712 + 12 n=1 36n4 + 9 lim by = 1 n-+00 O A. {by } is ultimately decreasing because the function f satifying f(n) = b,, is decreasing on the interval Therefore the series converges by the Alternating Series test. B. lim an = , so the series diverges by the Divergence Test. 71-100Use the Alternating Series Test to determine whether the series converges or diverges. (For limits, enter a number, "-infnity", "infinity", or "DNE" as appropriate.) DO n cos ( na) pun 1 1 lim by = 0 1 100 O A. {by } is ultimately decreasing because the function f satifying f(n) = b,, is decreasing on the interval Therefore the series converges by the Alternating Series test. OB. lim an = 0 so the series diverges by the Divergence Test. 71-100Use the Alternating Series Test to determine whether the series converges or diverges. (For limits, enter a number, "-infnity", "infinity", or "DNE" as appropriate.) DO 8(-1)" tan n n=1 lim bn = 16/pi 1-+00 O A. {ba } is ultimately decreasing because the function f satifying f(n) = b,, is decreasing on the interval Therefore the series converges by the Alternating Series test. B. lim an = 0 so the series diverges by the Divergence Test. 7100Given the convergent series, (-1)"+1 n=1 52n+1 (2n + 1)! How many terms are needed to approximate the sum of the series with |error)