Question

Evaluate the series ∑ from n=1 to infinity (-1)^n / n^4?
lim as n--> infinity absolute value of an+1/an = L

L=?



By ratio test, is it convergent?


is the series absolutely convergent, conditionally convergent or divergent?

Answer 1

by ratio test, An+1/An=(-1*(n/n+1)^4) -- > 0 as n-->inf. so the given summation is convergent

Answer 2

ok, but what is the value after evaluating