Question

Problem 1 convergence test used. Discuss convergence or divergence of the series. If convergent state the (a) ¿ In(n) In(n) In(n) + 2 n=1 (b) 2 (c)

Answer 1

Inn ed Sol inn Herd an Inn & 2 n=1 in n + 2 anti an ita In(n) le . an to Inn by nth terim test, 2 innti is dat D E n=2 Jn n-l Here ana Sn ny Now Get bna s = 1 #0 no nyo E JA Joilla) then lim an = lim bin So, by limit Comparision' test (LET) divergence of Ei implies divergence E 5 Hero 721 में bna 125 Ein is a. 6-f series and Therefore Convergent cs ans n. 21 ot then lim an lim 5 540 limits Now bo PA 721 Sol by LET, Es i convergent (in is convergent) dj E Halep Forte no ni lim un and and 5 (n+1)! is decreasing and anto so San Alternate series test wie Convergent char