In case you still remember your high school calculous, how can I prove that the infinite sum of k(1-x)^(k-1), k from 1 to ∞ is 1/(x^2) ?
@siah Note that -d/dx (1-x)^k is k(1-x)^(k-). So yr sum is -d/dx \sum (1-x)^k. But that sum is just 1/(1-(1-x)) = 1/x. Take derivative...
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@michael_nielsen@siah That was pretty similar to my answer. The key trick is noting that it's a derivative of terms that sum nicely. -
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