Please answer these qustions providing all the steps and explaination. there are related to Comparison Tests and alternating series

Suppose 25,, and 2b,, are series with positive terms and 2b,, is known to be oonvergent. (a) If anI :- b" for all n, what can you say about Ea\"? Why? Ea\" converges if and only if anI 3 4b\". 2 an diverges by ie Comparison Test. We cannot say anything about Ea\". 26\" converges if and only if anI 5 2b\". 2 an converges by the Comparison Test. (b) If an C. b" for all :1, what can you say about Ea\"? Why? 2 an diverges by ie Comparison Test. - 2 an converges by the Comparison Test. ' z - an converges If and only If T g an g b\". - We cannot say anything about Ea\". Ea\" converges if and only if h g an s b\". 2 Need Help? i Determine whether ie series converges or diverges. on n \"2:31 6n3 + 1 converges diverges \fTest the series for convergence or divergence. \"ff _1_[_)_)n 5_(n_)_ 4 = ?n + 4 Identify b\". Evaluate the following limit. lim bn nim Since Iim bn 0and banbu foraIIn.- nino Need Help? i i i Test the series for convergence or divergence. an E 3(1)"e-" n = 1 C;- oonverges i;- diverges Test the series for convergence or divergence. in: (1)\"sin(%) n = 1 Q;- converges -;;;' diverges Need rue-p? i i Test the series for convergence or divergence. C," converges a) diverges Need Help? i i Test the series for convergence or divergence. f: (_1]n+ 1 5 "=1 2n L_l- converges C) diverges If the series Is Convergent, use the Altemallng Series Estimation Theorem to determine how many terms we need tn) add In order to nd the sum with an error less than 0.00005. (If the quantity diverges, enter DIVERGES.) terms Approximate the sum of the series correct to four decimal places. Determine whether the series converges or diverges. n+1 Z m/E n=1 _' converges C;- diverges Need Help? i i Determine whether the series converges or diverges. no 2\" 2 3+3\" n=1 ' - converges Q diverges Determine whether the series converges or diverges. '_ " converges C;- diverges Need Help? i Determine whether the series converges or diverges. " '- converges Q diverges Need Help? i i Determine whether the series converges or diverges. no 2 i n! n = 1 C;- oonverges " '- diverges (a) What is an alternating series? An alternating series is a whose terms are . (b) Under what conditions does an alternating series converge? An alternating series 2 6n = Z (1)\" r 1b", where L7,, = Ianl, converges if 0