Solution (source code)

= Solution

The term at $k=0$ is finite. For every $k\geq1$,
$$
0<\frac1{1+k^2}\leq\frac1{k^2}.
$$
The comparison <P-series> $\sum k^{-2}$ converges, so the <comparison test for series> proves that \b[the given <series> converges absolutely].