Question

\(\frac{2}{5\cdot6\cdot7}+\frac{2}{7\cdot8\cdot9}+......................................+\frac{2}{99\cdot100\cdot101}\)

Answer 1

\(\frac{2}{5.6.7}+\frac{2}{7.8.9}+...+\frac{2}{99.100.101}\)

\(=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{99.100}+\frac{1}{100.101}\)

\(=\frac{1}{5.6}-\frac{1}{100.101}\)

\(=\frac{1007}{30300}\)

Answer 2

\(\frac{2}{5.6.7}\)+ \(\frac{2}{7.8.9}\)+...+\(\frac{2}{99.100.101}\)

= \(\frac{1}{5.6}\)- \(\frac{1}{6.7}\)+ \(\frac{1}{7.8}\)- \(\frac{1}{8.9}\)+ ... + \(\frac{1}{99.100}\)- \(\frac{1}{100.101}\)

= \(\frac{1}{5.6}\)- \(\frac{1}{100.101}\)= \(\frac{1007}{30300}\)

^_^ ( Have a good day )