Question

(1+1/1.3).(1+1/2.4).(1+1/3.5).........(1+1/99.101)

Answer 1

\(\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(\frac{1}{3.5.}\right).....\left(1+\frac{1}{99.101}\right)\)

\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.....\frac{10000}{9999}\)

\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.....\frac{100^2}{99.101}\)

\(=\frac{2^2.3^2.4^2.5^2.....98^2.99^2.100^2}{1.2.3^2.4^2.5^2......99^2.100.101}\)

\(=\frac{2.100}{1.101}\)

\(=\frac{200}{101}\)