\(\left(\dfrac{1}{2}+1\right)\left(\dfrac{1}{3}+1\right)...\left(\dfrac{1}{99}+1\right)\)
\(=\left(\dfrac{1+2}{2}\right)\left(\dfrac{1+3}{3}\right)\left(\dfrac{1+4}{4}\right)...\left(\dfrac{1+99}{99}\right)\)
\(=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}...\dfrac{100}{99}\)
\(=\dfrac{100}{2}=50\)
==(1+2/2)(1+3/3)(1+4/4)...(1+99/99)
=100/2=50