$\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\ldots 16$ terms $=$

Question

Aicharya · Accepted Answer

Given, $\begin{aligned} \frac{1}{2 \cdot 5} & +\frac{1}{5 \cdot 8}+\frac{1}{8 \cdot 11}+\ldots.16 \text { terms } \ & =\frac{1}{3}\left[\frac{3}{2 \cdot 5}+\frac{3}{5 \cdot 8}+\frac{3}{8 \cdot 11}+\ldots.\right] \ & =\frac{1}{3}\left[\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{5}-\frac{1}{11}+\ldots.+\frac{1}{47}-\frac{1}{50}\right] \ & =\frac{1}{3}\left[\frac{1}{2}-\frac{1}{50}\right]=\frac{1}{3}\left[\frac{48}{100}\right]=\frac{1}{3}\left[\frac{24}{50}\right]=\frac{8}{50}=\frac{4}{25} \end{aligned}$

\(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\ldots 16\) terms \(=\)

Solution