1. Apr 11, 2006

ArcainineFalls531

Compute the sum from k=0 to infinity of (k+1)(x)(1-x)^k.

I don't have any ideas about how to start this one, except that perhaps it resembles a geometric series? Also we're supposed to use the power series for 1/x which we know to be (1-x)^k. (That's all I could figure out on my own so far) What I could really use some help with is how to get started, then I should be able to pick it up from there. Thank you SO much for any help!

2. Apr 11, 2006

quasar987

hint: $(k+1)(1-x)^k = -\frac{d}{dx}(1-x)^k$