Question

Determine if the following Serie converges or not
\[\Large{\sum_{k\in\mathbb{N}}\frac{(-1)^{k}}{k^{2}+1}}\]

Answer 1

I suggest the alternating series test for this one.

Answer 2

how you should apply alternating series test to this serie ?

Answer 3

*would

Answer 4

Let's say the series is in the form \(\sum (-1)^nb_n\).
If \(b_n\) satisfies the following conditions:
1. \(b_n\) is decreasing, i.e. \(b_{n+1}<b_n\), and
2. \(\lim_{n \rightarrow \infty} b_n=0\),
then the series \(\sum (-1)^n b_n\) converges.

Answer 5

ist it Leipniz Criterium ?

Answer 6

Yeah, that's another name for this test.

Answer 7

ok thx =)