Question

A=(1+1/2) (1+1/3) (1+1/4)...(1+1/100)

Answer 1

\(\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)...\left(1+\dfrac{1}{100}\right)=\dfrac{3}{2}.\dfrac{4}{3}...\dfrac{101}{100}=\dfrac{101}{2}=50,5\)

Answer 2

\(\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)...\left(1+\dfrac{1}{100}\right)\\ =\left(\dfrac{2}{2}+\dfrac{1}{2}\right)\left(\dfrac{3}{3}+\dfrac{1}{3}\right)...\left(\dfrac{100}{100}+\dfrac{1}{100}\right)\\ =\dfrac{3}{2}.\dfrac{4}{3}...\dfrac{101}{100}\\ =\dfrac{3.4...101}{2.3...100}\\ =\dfrac{101}{2}\)