document.write( "Question 401421: how
\n" ); document.write( "(1+2p+3p^2+4p^3+................) is equal to (1-p)^-2 \n" ); document.write( "

Algebra.Com's Answer #284081 by richard1234(7193) $\"\"$ $\"About$

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. \n" ); document.write( "

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