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 $\sum\limits_{n=1}^{N}{\frac{1}{{{n}^{3}}}<\frac{11}{8}}$..[6]

Verify that $\frac{1}{2x}-\frac{1}{(x-1)}+\frac{1}{2(x-2)}=\frac{1}{x(x-1)(x-2)}$.

By using the above result, find $\sum\limits_{n=3}^{N}{\frac{1}{n(n-1)(n-2)}}$. Hence show that $\sum\limits_{n=1}^{N}{\frac{1}{{{n}^{3}}}<\frac{11}{8}}$..

Recurrence Relations and Summation

International Baccalaureate Higher Level Mathematics

2008 MJC P2 Q3 [Modified]

2008 MJC P2 Q3 [Modified]

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