Question

\(\frac{2}{5x8}+\frac{2}{8x11}+\frac{2}{11x14}+...+\frac{2}{95x98}\)

Answer 1

\(\frac{2}{5\times8}+\frac{2}{8\times11}+\frac{2}{11\times14}+...+\frac{2}{95\times98}\)

\(=\left(\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+...+\frac{3}{95\times98}\right)\times\frac{2}{3}\)

\(=\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{14}+...+\frac{1}{95}-\frac{1}{98}\right)\times\frac{2}{3}\)

\(=\left(\frac{1}{5}-\frac{1}{98}\right)\times\frac{2}{3}\)

\(=\frac{93}{490}\times\frac{2}{3}\)

\(=\frac{93\times2}{490\times3}\)

\(=\frac{31\times1}{245\times1}\)

\(=\frac{31}{245}\)