Question

determine if the series

((n^2+1)/(2n^2+1))^2n is absolutely convergent determine if the series

((n^2+1)/(2n^2+1))^2n is absolutely convergent @Mathematics

Answer 1

\[((n^2+1)/(2n^2+1))^{2n}\]

Answer 2

this \[\sum_{n=1}^{\infty}\left(\frac{n^2+1}{2n^2+1}\right)^{2n}\]

Answer 3

if so use the root test

Answer 4

\[\sum_{}^{}a_n \]

\[\lim_{n \rightarrow \infty}|a_n|^\frac{1}{n} \]

if less than one, then abs converges
if greater than one, then diverges
if =1, then inconclusive ( a waste of time and we are all very sad)

Answer 5

so whats the limit of the inside if n goes to infinity?

Answer 6

since the degrees inside are the same on both top and bottom then the limit inside is
( ? )^2
^
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