# Math Help - interval of convergence

1. ## interval of convergence

Interval of Convergence of the following...

2. Originally Posted by WartonMorton
Interval of Convergence of the following...

1) This question doesn't belong here

2) It's practically impossible to decypher what you meant to write, in particular that weird middle symbol...??

Tonio

3. Under the hypothesis that is...

$f(x)= \sum_{k=1}^{\infty} k a^{k} x^{k}$ (1)

... setting $a x = \xi$ we have...

$\sum_{k=1}^{\infty} k a^{k} x^{k}= \sum_{k=1}^{\infty} k \xi^{k}= \xi \sum_{k=1}^{\infty} k \xi^{k-1} = \xi \frac{d}{d \xi} \sum_{k=1}^{\infty} \xi^{k} =$

$= \xi \frac{d}{d \xi} \frac{\xi}{1-\xi} = \frac{\xi}{(1-\xi)^{2}}$ (2)

The series converges for $|\xi|<1$ ...

Kind regards

$\chi$ $\sigma$