## Compute the Sum

For students of class 11-12 (age 16+)
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### Compute the Sum

Let $a_0,a_1,a_2,...,a_{2011}$ is a series defined as $a_n=\frac{n}{2011}\; \; for\; \; n\ge 0$
Compute the sum $\sum_{k=0}^{2011}\; \frac{a_k^3}{1-3a_k+3a_k^2}$
Without using calculator or computer.

(It's one of the coolest APMO problems.Actually I needed only $5$ minutes to solve.So I think it will be a easy problem for Higher Secondary.)
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### Re: Compute the Sum

No reply!!! Is it so easy or hard that nobody tries?Well I'm giving a hint:
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*Mahi*
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### Re: Compute the Sum

I think the "too easy" part is true

Use $L^AT_EX$, It makes our work a lot easier!

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### Re: Compute the Sum

pairing yeids an elegant solution.