algebra with series

I

iDoof

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Oct 17, 2005
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I'm having trouble doing simple algebra with this series:

SUM (from n=0 to infinity) of c*x^n; where c is some constant.

Say this entire series is multiplied by x. I know that I can pull that x into the SUM by adding 1 to the exponent of the x inside the SUM. But what if I want to keep that x^n factor? I also want the index of the SUM to remain the same (from n=0). What manipulations are possible to do this?

Thanks for your time everyone!
 
Why would you want to maintain x<SUP>n</SUP> and the index after multiplying the series by x? I don’t think you can do both.
 
I thought I must just be missing something, but pka echoed my questions regarding your post.

Is your summation perhaps part of a larger exercise? If so, could you please post the entire context?

Thank you.

Eliz.
 
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