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20warriorsoul14

08.03.2020

Mathematics

Perhaps it suffices to say that

$\displaystyle\frac1{1^2}+\cdots+\frac1{n^2}=\sum_{k=1}^n\frac1{k^2}$

converges to $\frac{\pi^2}6$ as $n\to\infty$ , while $n^3\to\infty$ . Then

$\displaystyle\lim_{n\to\infty}a_n=\infty\cdot\frac{\pi^2}6=\infty$

so a_n diverges.

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