SOLUTION: how (1+2p+3p^2+4p^3+................) is equal to (1-p)^-2

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Question 401421: how
(1+2p+3p^2+4p^3+................) is equal to (1-p)^-2
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
I solved a problem very similar to this one. The infinite series can be expressed as (1+p+p^2+...) + (p+p^2+p^3+...) + (p^2+p^3+p^4+...) = (1+p+p^2+p^3+...)(1+p+p^2+p^3+...) = %28sum%28p%5Ei%2C+i+=+0%2C+infinity%29%29%5E2. The sum of a geometric series sum%28p%5Ei%2C+i+=+0%2C+infinity%29 is given by 1%2F%281-p%29+=+%281-p%29%5E%28-1%29, so squaring it, we obtain %281-p%29%5E-2. Note that -1+%3C+p+%3C+1 for this to occur, as the series diverges otherwise.