Question

What is the value of the following expression?
$\left(\frac{1}{2^2-1}\right)+\left(\frac{1}{4^2-1}\right)+\left(\frac{1}{6^2-1}\right)+\left(\frac{1}{{20}^2-1}\right)$

• A. $\frac{9}{19}$
• B. $\frac{172}{399}$
• C. $\frac{10}{21}$
• D. $\frac{11}{21}$

Answer 1

The correct option is B $\frac{172}{399}$

$\frac{1}{(2^2-1)}+\frac{1}{(4^2-1)}+\frac{1}{(6^2-1)}+\frac{1}{({20}^2-1)}=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{399}$

$\Rightarrow \frac{(399\times 15\times 35)+(399\times 3\times 35)+(3\times 15\times 399)+(3\times 15\times 35)}{399\times 35\times 15\times 3}$

$=\frac{270900}{628425}=\frac{172}{399}$