I was doing some practice problems and everything was going great till I saw this question out of the ordinary: $$ f(x,y) = \sum_{n=0}^\infty(xy)^n \qquad \left|xy\right| < 1 $$ Any thoughts on how to do this?

I know that the general formula should be something like this: Differentiate with respect to $x$: $nx^{n-1}y^n$

But this whole summation thing really confuses me as I am not 100% sure what to do.

  • $\begingroup$ Just sun the series first as in then hint and the find the derivative. $\endgroup$ – Mhenni Benghorbal Sep 27 '13 at 7:14
  • $\begingroup$ would it be converge to 1/(1-xy) ?? $\endgroup$ – Raynos Sep 27 '13 at 13:34

Hint: This sum is a geometric series.

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