I have arrived at a expression $\sum_{n=0}^{\infty}n(n-1)(x^n +x^{n-1})$ in a Maclaurin series question.
Is this a suitable form? If not, how do I adjust what I already have?
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No. You need to combine the $x^n$ and $x^{n-1}$. – Jacky Chong Oct 01 '16 at 09:02
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May I ask how? Apologies if this is an absent minded question... – Hugh Entwistle Oct 01 '16 at 09:03
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It is not clear from your expression what's the coefficient of, say, $x^7$, so it is not a suitable form. – mercio Oct 01 '16 at 09:10
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But similarly, isn't it also unclear to read off the coefficient of $x^7$ from the expression given as an answer? You still need to inspect when $n=7,8$ ? – Hugh Entwistle Oct 01 '16 at 09:12
1 Answers
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$$\sum_{n=0}^{\infty}n(n-1)(x^n +x^{n-1})=\sum_{n=0}^{\infty}n(n-1)(x^n+\frac{x^n}{x})=(1+\frac{1}{x})\sum_{n=0}^{\infty}n(n-1)x^n$$
E.H.E
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