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Let $S_n$ represent its partial sum, and let $s$ represent its value. Prove that $s$ is finite and find and an $n$ so large that $S_n$ approximates s to 3 decimal places. $$\sum_{k=1}^{\infty}\left(\frac{k}{k+1}\right)^{k^2}$$

Solution we use root test i think. But how to calculate this? Thanks.

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