\(=\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times....\times\frac{99}{98}\times\frac{100}{99}\)
\(=\frac{3.4.5....99.100}{2.3.4....99}\)
\(=\frac{100}{2}=50\)
\(\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)....\left(1+\frac{1}{99}\right)\)
\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}....\frac{100}{99}\)
\(=\frac{3.4.5....100}{2.3.4....99}\)
\(=\frac{100}{2}=50\)
=3/2x4/3x5/4x6/5x............x100/99
=100/2=50