Question

1/1x6 + 1/6x11 +...+ 1/96x101

Answer 1

\(\frac{1}{1.6}+\frac{1}{6.11}+...+\frac{1}{96.101}\)

\(=\frac{1}{5}.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{96}-\frac{1}{101}\right)\)

\(=\frac{1}{5}.\left(1-\frac{1}{101}\right)\)

\(=1.\frac{100}{101}\)

\(=\frac{100}{101}\)