if Σ∣a_n ∣ is convergent, then prove that there exists a subsequence {n_k a_n_k } with lim_(k→∞) n_k a_n


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Question Number 63054 by jimful last updated on 28/Jun/19
$if Σ∣a_n ∣ is convergent, then prove that there exists a subsequence {n_k a_n_k } with lim_(k→∞) n_k a_n_k =0$
$i f Σ ∣ a_{n} ∣ i s c o n v e r g e n t, t h e n$ $p r o v e t h a t t h e r e e x i s t s$ $a s u b s e q u e n c e {n_{k} a_{n_{k}}} w i t h$ $\lim_{k \to \infty} n_{k} a_{n_{k}} = 0$
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