SOLUTION: Find the sum of n terms of series 1+3x+5x^2+7x^3+.........

Question 1083331: Find the sum of n terms of series 1+3x+5x^2+7x^3+.........
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

Let S = the sum of the first n terms of the given sequence.

The nth term will have coefficient (2n-1) and (n-1)st power of x.
So we have:



Multiply the sequence through by -x and add term by term to
the given sequence:



Can you finish from here?:



The n-1 terms between the first and last ones form a geometric 
series.  Use a formula for them, then you can solve for S.

If you have trouble, tell me in the thank-you note form below 
and I'll get back to you by email.  No charge as I do this
for fun.

Edwin

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