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

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

anonymous · Answer

$$((n^2+1)/(2n^2+1))^{2n}$$

zarkon · Answer

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

zarkon · Answer

if so use the root test

myininaya · Answer

$$\sum_{}^{}a_n   $$

$$\lim_{n \rightarrow \infty}|a_n|^\frac{1}{n}   $$

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)

myininaya · Answer

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

myininaya · Answer

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