Question

(1+1/2)×(1+1/3)×(1+1/4)×...×(1+1/100)

Answer 1

\(=\dfrac{3.4.5...101}{2.3.4...100}=\dfrac{101}{2}\)

Answer 2

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

\(=\dfrac{101}{2}\)