MAC-2312 Lecture 37: Study Guide 37 (Test for Divergence for Series)

(1 point) Match the following series with the series below in which you can compare using the Limit Comparison Test. Then determine whether the series converge or diverge c0 and Does this series converge or diverge?? n+ 2 2. Does this series 3 (n +1)2 converge or diverge?? 3 Does this series n-2 converge or diverge?? 4 Does this series 2n2 +1 converge or diverge??

(a) Find the interval of convergence for the following: Σ r" R+ n=0 (b) Determine whether the alternating series converges or diverges by using the alternating series test: In-1 n-1 2 n=1 (c) Use the ratio test to determine whether the series is absolutely convergent, conditionally conver- gent, or divergent: Σ(-1)"

) Find the exact sum of the series, if possible. Σ.3 ) Determine if the following series converge or diverge. using, and show all of your work. 3n 72 c) 1(2n)!(n-1). C-1)n+i oo cos(nn) f) Σ 1nti ( n+1 use Divergence Test, lim--= 1 oo Inn Determine whether the series is absolutely conven