prove that ∀n∈N^★ (1/(√n)) −(1/(√(n+1))) ≥ (1/(2(n+1)(√(n+1)))) 2) prove that u_n = Σ


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Question Number 30217 by abdo imad last updated on 18/Feb/18

$p r o v e t h a t \forall n \in N^{★} \frac{1}{\sqrt{n}} - \frac{1}{\sqrt{n + 1}} ⩾ \frac{1}{2 (n + 1) \sqrt{n + 1}}$ $2) p r o v e t h a t u_{n} = \sum_{k = 1}^{n} \frac{1}{k \sqrt{k}} i s c o n v e r g e n t e .$
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