Suppose {$a_n$} is a sequence with $a_n>0$. For each $k$ in $\Bbb{N}$, set $$b_k = \frac{1}{k} \sum_{n=1}^{k}a_n$$ then woud $\sum_{k=1}^{\infty}b_k$ always diverge?
I want to use Converge Tests for proof, but I don't know what to use.
2026-03-29 13:46:39.1774791999
Series of Sequence which always diverges
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Hint: $b_k \geq \frac{a_1}{k}$, because $a_n > 0$ for all $n$.