pt x din [0,1] evident sirul este descrescator
[tex]x^{n} \geq x^{n+1}\\\frac{x^{n}}{x^{2}+1} \geq \frac{x^{n+1}}{x^{2}+1} \\integram... \\I_{n} \geq I_{n+1}[/tex]
de asemenea se arata ca sirul este marginit
[tex]0 \leq x^{n} \leq 1\\0 \leq \frac{1}{x^{2}+1} \leq \frac{1}{2} \\0 \leq \frac{x^{n}}{x^{2}+1} \leq \frac{1}{2} \\integram...\\0 \leq I_{n} \leq \frac{1}{2}\\[/tex]
Sir marginit+monoton =>admite limita iar:
[tex]\lim_{n \to \infty} I_n=L[/tex]
