Question

The sum of the series ${\sum }_{r=2}^{25}\frac{1}{(r^2-1)}$ is-

• A. $\frac{231}{325}$
• B. $\frac{232}{325}$
• C. $\frac{231}{327}$
• D. $Noneofthese$

Answer 1

The correct option is A $\frac{231}{325}$

Given

${\sum }_{r=2}^{25}\frac{1}{r^2-1}$

Put $r=2,3,4,\mathrm{5.....25}$ accordingly and get the values

$=\frac{1}{3}+\frac{1}{8}+\frac{1}{15}+\frac{1}{24}+\frac{1}{35}+\frac{1}{48}+\frac{1}{63}+\frac{1}{80}+\frac{1}{99}+\frac{1}{120}+\frac{1}{143}+\frac{1}{168}+\frac{1}{195}+\frac{1}{224}+$

$+\frac{1}{255}+\frac{1}{288}+\frac{1}{323}+\frac{1}{360}+\frac{1}{399}+\frac{1}{440}+\frac{1}{483}+\frac{1}{528}+\frac{1}{575}+\frac{1}{624}$

$=\frac{231}{325}$