prove that : Σ_(n=1) ^∞ (( cos( n ))/n) ( 1+(1/( (√2))) + (1/( (√3))) + ...+(1/( (√n))) ) is convergent.


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Question Number 216274 by mnjuly1970 last updated on 02/Feb/25

$p r o v e t h a t :$ $\underset{n = 1}{\sum^{\infty}} \frac{c o s (n)}{n} (1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + . . . + \frac{1}{\sqrt{n}})$ $i s c o n v e r g e n t .$
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