Discussion Forum

Find the value of $\frac{3}{1^{2}.2^{2}}+\frac{5}{2^{2}.3^{2}}+\frac{7}{3^{2}.4^{2}}+\frac{9}{4^{2}.5^{2}}+\frac{11}{5^{2}.6^{2}}+\frac{13}{6^{2}.7^{2}}+\frac{15}{7^{2}.8^{2}}+\frac{17}{8^{2}.9^{2}}+\frac{19}{9^{2}.10^{2}}$

Answer:

Explanation:

Given exp.
$=\left(\frac{1}{1^{2}} - \frac{1}{2^{2}}\right) + \left(\frac{1}{2^{2}} - \frac{1}{3^{2}}\right) + \left(\frac{1}{3^{2}} - \frac{1}{4^{2}}\right)+\left(\frac{1}{4^{2}} - \frac{1}{5^{2}}\right)+.....+\left(\frac{1}{9^{2}} - \frac{1}{10^{2}}\right)$
$=\left(\frac{1}{1^{2}} - \frac{1}{10^{2}}\right) =\left(1-\frac{1}{100} \right)$
$=\frac{99}{100}$