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I need help with understanding how to solve this task, because I'm a bit lost at the moment.

Use the powerseries $$f(x)=\frac{1}{1-x}$$ to decide the sum of the series

$\sum_{n=1}^{\infty} n(n+1)x^n$ and $\sum_{n=1}^{\infty} \frac{n(n+1)}{3^n}$

I don't understand how to manipulate the sums to use the power series of the function.

Answers