I am learning about series of numbers at the moment. In the book there is an exercise in which I need to find the sum of : $$\sum_{i=1}^{\infty}\frac{i}{2^i}$$ I know it is equal to $2$. But how do I get to that result? Are there any general ways of finding the sums of series? In the books I am using, there is a lot about series, their convergence etc. but almost no examples.
I don't do math a long time, so I completely don't remember how to prove that: $$ \sum_{i=1}^\infty \frac{i}{2^i} = 2 $$  Can anybody help me?
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