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Hi all What would the best way/method be to approach this, any advice would be appreciated

otupygak
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  • Binomial theorem might help – Jasser Oct 07 '14 at 10:27
  • Thank you very much @Travis Ive got it now – otupygak Oct 07 '14 at 10:31
  • I wonder how the binomial theorem can help here. – Timbuc Oct 07 '14 at 10:32
  • @Kimo You're welcome, I'm glad you found the link useful. – Travis Willse Oct 07 '14 at 10:33
  • @Timbuc you can see the answer below which has an expansion of 1 over 1-x. – Jasser Oct 07 '14 at 10:42
  • @user291957, that's the expansion of a function in a power series. What that has to do with the binomial theorem, which states that $$\forall,a,b\in\Bbb R,,,n\in\Bbb N;,;;(a+b)^n=\sum_{k=0}^n\binom nk a^{n-k}b^k;?$$ While certainly one can try to expand that theorem to the case where $;n\notin\Bbb N;$, that's not usually known as "the binomial theorem", imo. – Timbuc Oct 07 '14 at 11:20

1 Answers1

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Notice:

$$ \frac{1}{1-x} = \sum x^n $$

By Abel's theorem, we can differentiate the series, and we obtain

$$ \frac{1}{(1-x)^2} = \sum n x^{n-1}$$

Now, you should conclude.