Verify that $\frac{1}{2x}-\frac{1}{(x-1)}+\frac{1}{2(x-2)}=\frac{1}{x(x-1)(x-2)}$. [1] By using the

Question

Verify that $\frac{1}{2x}-\frac{1}{(x-1)}+\frac{1}{2(x-2)}=\frac{1}{x(x-1)(x-2)}$. [1] By using the above result, find $\sum\limits_{n=3}^{N}{\frac{1}{n(n-1)(n-2)}}$. Hence show that $\sum\limits_{n=1}^{N}{\frac{1}{{{n}^{3}}}[6]

Accepted Answer

$\sum_{n=3}^N\frac1{n(n-1)(n-2)}=\frac14-\frac1{2(N-1)}+\frac1{2N}$, and $\sum_{n=1}^N\frac1{n^3}<\frac{11}{8}$

2008 MJC P2 Q3 [Modified]

2008 MJC P2 Q3 [Modified]

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