Express $\frac{2}{x(x-1)(x-2)}$ in partial fractions. By using the above result, show that \(

Question

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 $\sum\limits_{n=1}^{\infty }{\frac{1}{n^{3}}} \le 1 + \frac{b}{a^{b}}$.

Accepted Answer

$a = 2$, $b = 3$

Practice 2 Q1

Practice 2 Q1

Solution:

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