prove-that-n-N-1-n-1-n-1-1-2-n-1-n-1-2-prove-that-u-n-k-1-n-1-k-k-is-convergente-

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 .