Express $\frac{2}{x(x-1)(x-2)}$ in partial fractions.

By using the above result, show that
$\sum\limits_{n=3}^{N}{\frac{1}{n^{3}}} \le \frac{1}{4} - \frac{1}{2N(N-1)}$.

Hence find $a$ and $b$ such that
$\sum\limits_{n=1}^{\infty }{\frac{1}{n^{3}}} \le 1 + \frac{b}{a^{b}}$.

Express $\frac{2}{x(x-1)(x-2)}$ in partial fractions.


By using the above result, show that
$\sum\limits_{n=3}^{N}{\frac{1}{n^{3}}} \le \frac{1}{4} - \frac{1}{2N(N-1)}$.


Hence find $a$ and $b$ such that
$\sum\limits_{n=1}^{\infty }{\frac{1}{n^{3}}} \le 1 + \frac{b}{a^{b}}$.

Recurrence Relations and Summation

H2 Math

International Baccalaureate Higher Level Mathematics

Practice 2 Q1

Practice 2 Q1