Wikipedia: Algebraic derivation of mean says:

Sure, is "a discrete random variable", but does that inevitably mean that ? Couldn't all be, say, multiples of 3 ( )?

And in next step they use this to saywhich is an essential part of proving that if (which is why I'd like to understand why should ).The first term of the series (with indexk= 0) has value 0 since the first factor,k, is zero.