Question

Determine whether the following series are absolute convergent, conditionally convergent or divergent? º 2+,(-1) Explain your reasoning. Your answer must include the name of the series test and explicitly show that all the condition are met.

Please provide all the steps and answer all of the question! Thank you!

Answer 1

For checking the convergence of given series, we shall use following results - 0 A series {un is absolutely convergent if sllant is convergent © Every absolutely onvergent sonjes de convergent (3) sum of two convergent series is convergent. @ the geometrie series is ann is convergent if l»l<1 . T=0 where, a=ist term n= common natio. Given series is – Now, he is a geometric series with common ratio, se Now, f) - 41 So, , ha is convergent (170) again, they are one, with team un sayang Now, I s nie, Ella) = 24h is also a geometrie series with common ratio, vel (1 - is absolutely onvergent (170) --) is convergent (by @) then from and both, the given series is convergent. but not absolutely convergent's) conditionally convergent.