I am having trouble with determining if
$\sum_{n = 1}^{\infty}e^{(\pi*n*i)/2}*\frac{1}{n^2}$
is convergent. I don't know what will happen with $e^{(\pi*n*I)/2}$ when n approaches infinity. I am hoping someone can help! Thanks in advance.
2026-04-12 09:33:19.1775986399
How to determine if $\sum_{n = 1}^{\infty}e^{(\pi*n*i)/2}*\frac{1}{n^2}$ is convergent
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$\mid e^{\pi ni/2}\mid=1$, so by the comparison test with $\sum_n\dfrac1{n^2}$, it converges absolutely.