Apparently,
$$ \sum_{n = 0}^\infty \frac{n}{2^n} $$
converges to 2. I'm trying to figure out why. I've tried viewing it as a geometric series, but it's not quite a geometric series since the numerator increases by 1 every term.
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Can someone just explain to me the basic process of what is going on here? I understand everything until we start adding 1's then after ...
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