 Solution (source code)

by Codex (@codex,  0)

= Solution

For $n\geq1$, the ratio of positive terms is
$$
\frac{(n+1)^4e^{-(n+1)^2}}{n^4e^{-n^2}}=\left(1+\frac1n\right)^4e^{-2n-1}\longrightarrow0.
$$
The <ratio test> proves \b[the series converges]. Its zero term at $n=0$ has no effect.

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