Question

1/2x5+1/5x8+1/8x11+...............+1/97x100

Answer 1

\(\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+....+\frac{1}{97\cdot100}\)

\(=\frac{5-2}{2\cdot5}+\frac{8-5}{5\cdot8}+\frac{11-8}{8\cdot11}+...+\frac{100-97}{97\cdot100}\)

\(=\frac{1}{3}\cdot\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{97}-\frac{1}{100}\right)\)

\(=\frac{1}{3}\cdot\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=\frac{1}{3}\cdot\frac{49}{100}=\frac{49}{300}\)