Express $\frac{r}{(2r-1)(2r+1)(2r+3)}$ in partial fractions. Hence find the sum of the first terms

Question

Express $\frac{r}{(2r-1)(2r+1)(2r+3)}$ in partial fractions. Hence find the sum of the first terms of the series $S_n=\frac{1}{1\cdot 3\cdot 5}+\frac{2}{3\cdot 5\cdot 7}+\frac{3}{5\cdot 7\cdot 9}+\dots$ and show that $S_n<\frac{1}{8}$.

Accepted Answer

$S_n < \frac{1}{8}$

Application of Sum to Infinity Q2

Application of Sum to Infinity Q2

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