Question

2/5x9 + 2/9x13 + 2/13x17 +....+ 2/55x59

 

Answer 1

\(\frac{2}{5.9}+\frac{2}{9.13}+\frac{2}{13.27}+...+\frac{2}{55.59}\)

\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{27}+...+\frac{1}{55}-\frac{1}{59}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{59}\right)\)

\(=\frac{1}{2}.\frac{54}{295}\)

\(=\frac{27}{259}\)