Ok, so I have the sums 1/2(n^(2)-n)x^(n-1) + 1/2(n^(2)-n)x^(n-1) from n=2. The next part of the question says I should relate (n^2)/(2^n) to the previous equation. Is there a simplification I'm missing?
Oh wow. Thanks for your help, I guess my brain is rebelling against obvious steps. :blushing:
Ok, so now I have the sum of (n^2-n)x^(n-1) + sum of (n^2-n)x^n, both starting from n=2, and both expressions multiplied by 1/2.
I tried to find a power expansion for that term and found it as 2(1-x)^3, which would equal the power series (n^(2)-n)x^(n-2) from n=2. From here, I'm not sure if there is an equation for the numerator, or if there is a way to multiply the numerator into this equation in a way that makes sense.
Homework Statement
Expand f(x)= (x+x2)/(1-x)3
Homework Equations
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The Attempt at a Solution
I've tried everything I can think of to simplify this equation: substitution of various other power series, partial fraction decomposition, taking derivatives, multiplying out the...