Question

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

• A. $\frac{4}{25}$
• B. $\frac{8}{25}$
• C. $\frac{16}{25}$
• D. $\frac{1}{25}$

Answer 1

Answer: (A)

Given,
$\frac{1}{2 \cdot 5} +\frac{1}{5 \cdot 8}+\frac{1}{8 \cdot 11}+\ldots .16 $ 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} $