exo7 5446

Limites de $$\begin{array}{llll} 1)\;\frac{1}{n^3}\sum_{k=1}^{n}k^2\sin\frac{k\pi}{n}&2)\;(\frac{1}{n!}\prod_{k=1}^{n}(a+k))^{1/n}\;(a>0\;\mbox{donné})&3)\;\sum_{k=1}^{n}\frac{n+k}{n^2+k}&4)\;\sum_{k=1}^{n}\frac{1}{\sqrt{n^2-k^2}}\\ 5)\;\frac{1}{n\sqrt{n}}\sum_{k=1}^{n}E(\sqrt{k})&6)\;\sum_{k=1}^{n}\frac{k^2}{8k^3+n^3}&7)\;\sum_{k=n}^{2n-1}\frac{1}{2k+1}&8)\;n\sum_{k=1}^{n}\frac{e^{-n/k}}{k^2} \end{array}$$