
two series questions
Hi all,
I had two questions
1. $\displaystyle \sum ^{\infty}_{i=1} \frac{1}{\left(i1\right)!} \frac{d}{d\lambda} \left(\lambda^{i}\right)= \frac{d}{d\lambda} \sum ^{\infty}_{i=1} \frac{1}{\left(i1\right)!} \lambda^{i} $
2. $\displaystyle \sum^{\infty}_{x=1} x r^{x} = \frac{r}{\left(1r\right)^{2}}$
why are 1 and 2 true
For the first I think it has to do with the radius of convergence.
Can someone help to prove this,
Thank you very much

1. Power series  Wikipedia, the free encyclopedia
2.
$\displaystyle \sum\limits_{x = 1}^\infty {xr^x } = r\sum\limits_{x = 1}^\infty {xr^{x  1} = } r\sum\limits_{x = 1}^\infty {\frac{d}
{{dr}}r^x = } r\frac{d}
{{dr}}\sum\limits_{x = 1}^\infty {r^x = } r\frac{d}
{{dr}}\frac{r}
{{1  r}} = \frac{r}
{{\left( {1  r} \right)^2 }}
$

thanks for the help
I already solved the first now and thanks for the seccenodn )it was the same mechanism (Hi)