I have this series and I need to determine whether it is divergent or convergent, are my calculations correct and it is divergent or am I not seeing something
$$ \sum_{n=2}^\infty (-1)^n \left( \frac{n}{2n+1}\right)^2 $$ since it is an alternating series I find the limit of a_n $$ \lim_{n\to \infty}\left( \frac{n}{2n+1}\right)^2 = \frac{n^2}{(2n+1)^2} = \frac{n^2}{4n^2+4n+1} = \frac{1}{4} $$ and since it does not equal to 0 by the alternating divergence test it s divergent ??
from Hot Weekly Questions - Mathematics Stack Exchange
GregoryStory16
Post a Comment