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Étudier la convergence des suites :
\(\sqrt{n^2 + n + 1}-\sqrt n \qquad \dfrac{n\sin (n)}{n^2 + 1} \qquad \dfrac1n + (-1)^n
\qquad n \sum\limits_{k = 1}^{2n + 1}\dfrac 1{n^2 + k} \qquad
\dfrac 1n \sum\limits_{k = 0}^{n-1}\cos (\dfrac1{\sqrt{n + k}})\)