CSSA Trials: Maths (1 Viewer)

Davo_01 · Jul 31, 2014

panakap said:
Post all the specific question on a CSSA thread I got.

Poll there as well :thumbsup:

Il finish the sols here first then il move it lol

integral95 · Jul 31, 2014

Davo_01 said:
$$i) Show that$ \dfrac{x^{2^n}}{1-x^{2^{n+1}}}=\dfrac{1}{1- x^{2^n}}-\dfrac{1}{1-x^{2^{n+1}}}$

$$ii) Hence show that$ \sum_{n=0}^{N} \dfrac{x^{2^n}}{1-x^{2^{n+1}}}=\dfrac{1}{1-x}-\dfrac{1}{1-x^{2^{N+1}}}$

$$iii)Given that$ \lim_{n\rightarrow \infty}\sum_{n=0}^{N} \dfrac{x^{2^n}}{1-x^{2^{n+1}}}=\sum_{n=0}^{\infty} \dfrac{x^{2^n}}{1-x^{2^{n+1}}}\; $and$\; -1<x<1$

$$Hence show that $ \sum_{n=0}^{\infty} \dfrac{x^{2^n}}{1-x^{2^{n+1}}}=\dfrac{x}{1-x}$

$$iv)Evaluate$ \sum_{n=0}^{\infty} \dfrac{1}{2014^{2^n}-2014^{-2^n}}$

Great memory indeed, lol aren't you in uni?, how did you get to see the paper?

Davo_01 · Jul 31, 2014

integral95 said:
Great memory indeed, lol aren't you in uni?, how did you get to see the paper?

pm'd

CSSA Trials: Maths (1 Viewer)

Davo_01

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integral95

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