how to calculate the serires i*(1/6)^i, i from 0 to infinite?

[W_Heisenberg]

Need help!

 

[_Eduardo_]

Hint: \[\dfrac{1}{1-x}=\displaystyle\sum_{i=0}^{\infty}{x^i}\;\;\longrightarrow\;\;\dfrac{d}{dx}\left(\dfrac{1}{1-x}\right)=\dfrac{1}{(1-x)^2}=\displaystyle\sum_{i=0}^{\infty}{i\;x^{i-1}=\dfrac{1}{x}\displaystyle\sum_{i=0}^{\infty}{i\;x^i}\]

 

[W_Heisenberg]

wow, this is smart!
thanks a lot, buddy