Calculus II unit 11 test review practice

please maybe an explanation of the entire process and show all work too? Thank you so much!

Name: Class: Date: ID: A Unit 11 practice Numeric Response 1. Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. 1/2, -4/3,9/4,-16/5, 25/6,... 2. Use the Integral Test to determine whether the series is convergent or divergent. 1 8 E 8n + 1 n = 1 3. Determine whether the sequence converges or diverges. If it converges, find the limit. an = 2e2n/ (n+ 2) 4. Determine whether the series is convergent or divergent by using partial fratcions to express the series as a telescoping sum. If it is convergent, find its sum. M n=In+ 3n 5. Use the alternating series test to test the series for convergence or divergence. (- 3 ) k+ 1 k = 1 42kName: ID: A 6. Use the test for absolute convergence and the root test to determine Whether the series is absolutely convergent, conditionally convergent, or divergent. n n2+2 3n2+2 00 Z n: 7. Use the comparison test with 2x" to nd the interval and radius of convergence of the series. 71:] no nrr 2 8x 2 n=1(n+5) 8. Find a power series representation for the function and determine the radius of convergence. f(x) = arctan[] 9. Find the Maclaurin series for f and its radius of convergence. f(x) = 111(1 x) 10. Find the Taylor series for f (x) centered at the given value of a. Assume that f has a power series expansion. Also nd the associated radius of convergence. x) =x43x2+l, a=l