| (Oral Ccp) On pose {u_{n}=\displaystyle\int_{0}^{1}x^{n}\sin (\pi x)\,\text{d}x}. Étudier la convergence de {\displaystyle\sum_{n\ge0} u_{n}}. Montrer que : {\displaystyle\sum\limits_{n=0}^{+\infty }u_{n}=\displaystyle\int_{0}^{\pi }\dfrac{\sin t}{t}dt}. |