Question

\(\left(1+\frac{1}{2}\right)\cdot\left(1+\frac{1}{3}\right)\cdot\left(1+\frac{1}{4}\right)\cdot....\cdot\left(1+\frac{1}{98}\right)\cdot\left(1+\frac{1}{99}\right)=\)?

Answer 1

\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)...\left(1+\frac{1}{99}\right)=\frac{3}{2}.\frac{4}{3}...\frac{100}{99}=\frac{100}{2}=50\)

Answer 2

 = \(\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot\cdot\cdot\cdot\frac{99}{98}\cdot\frac{100}{99}=\frac{3.4.5....99.100}{2.3.4....98.99}=\frac{100}{2}=50\)

Answer 3

\(\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right).........\left(1+\frac{1}{99}\right)\)

\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.....\frac{99}{98}.\frac{100}{99}\)

\(=\frac{3.4.5....99.100}{2.3.4.5....98.99}\)

\(=\frac{100}{2}\)

\(=50\)