Limit of sum-fonction

**dhiab** · June 22nd 2009, 06:52 AM

For all naturel number n .

the function :
Calculate :

**Plato** · June 22nd 2009, 07:49 AM

Isn't clear that $f_n (x) = \sum\limits_{k = 0}^n {\frac{{x^2 }}{{\left( {1 + x^2 } \right)^k }}} ?$

Also that $\left( {\forall x} \right)\left[ {\frac{1}{{\left( {1 + x^2 } \right)}} \leqslant 1} \right]$ .

**Raoh** · June 22nd 2009, 09:14 AM

hi

$\frac{x^{2}}{(1+x^{2})^{n}}$ $\to 0$
while $n \to +\infty$
i might be wrong,i'm just trying to help

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