Let $f(x) = {2 \over {1-2x}}$.
How can you tell the expansion is: $\{2x + 2^2x^2 + 2^3x^3 + ...\}$
I am familiar with the geometric series and I guess there must be a connection between the two.
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$$f(x)=\frac{2}{1-2x}=2\sum_{k=0}^\infty 2^k x^k=2+2^2x+2^3x^2+\cdots$$
J.R.
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Hmm.. How can one know that $1 \over {1-2x}$ is equal to $\sum 2^kx^k$. it looks like out of the blue to me. – AnnieOK Mar 04 '14 at 11:42
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Geometric series... $1+x+x^2+\ldots=\frac1{1-x}$ – user2345215 Mar 04 '14 at 11:42
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Oh right. I got it now. – AnnieOK Mar 04 '14 at 11:43