Question

Determine if the following series is convergent or divergent.

Answer 1

\[\sum_{n=0}^{\infty}(-1)^n/n^2+1\]

Answer 2

do u know the first comparison test??????

Answer 3

yeah

Answer 4

this ques can be done by first comparison test
but this is an alternating series so first comparison test cannot be applied here
therefore , we need to apply Leibnitz test

Answer 5

According to Leibnitz test , If an alternating series (-1)^n Un satisfies
(1) Un+1≤ Un for all values of n { here "n" is in subscript}
(2) lim Un = 0 as n tend into ∞
then the series (-1)^n Un converges

Answer 6

@mustry in order to make the given series convergent we need to satisfy the above conditions

Answer 7

okay

Answer 8

@mustry can u do this ques now??????

Answer 9

its difficult may be later !!!

Answer 10

in order to prove the first condition,
we know
(n+1)^2 + 1 ≥ n^2 + 1 for all values of n
1/(n+1)^2 + 1 ≤ 1/n^2 + 1 for all values of n
from above it is concluded that
Un+1 ≤ Un for all values of n

Answer 11

@mustry did u follow the proof of first cndition????