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[ex:rou1ter] Nature de la série de terme général
| 1) (*) \(\ln\left(\frac{n^2+n+1}{n^2+n-1}\right)\) | 2) (*) \(\frac{1}{n+(-1)^n\sqrt{n}}\) | 3) (**) \(\left(\frac{n+3}{2n+1}\right)^{\ln n}\) | 4) (**) \(\frac{1}{\ln(n)\ln(\ch n)}\) |
| 5) (**) \(\Arccos\sqrt[3]{1-\frac{1}{n^2}}\) | 6) (*) \(\frac{n^2}{(n-1)!}\) | 7) \(\left(\cos\frac{1}{\sqrt{n}}\right)^n-\frac{1}{\sqrt{e}}\) | 8) (**) \(\ln\left(\frac{2}{\pi}\Arctan\frac{n^2+1}{n}\right)\) |
| 9) (*) \(\int_{0}^{\pi/2}\frac{\cos^2x}{n^2+\cos^2x}\;dx\) | 10) (**) \(n^{-\sqrt{2}\sin(\frac{\pi}{4}+\frac{1}{n})}\) | 11) (**) \(e-\left(1+\frac{1}{n}\right)^n\) |