\(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{101}{100}=\dfrac{101}{2}\)
\(A=\left(1+\dfrac{1}{2}\right)\times\left(1+\dfrac{1}{3}\right)\times\left(1+\dfrac{1}{4}\right)\times...\times\left(1+\dfrac{1}{100}\right)\\ \Rightarrow A=\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times\text{}\text{}\text{}...\times\dfrac{101}{100}\\ \Rightarrow A=\dfrac{3}{3}\times\dfrac{4}{4}\times...\times\dfrac{101}{2}\\ \Rightarrow A=1\times1\times...\times\dfrac{101}{2}\\ \Rightarrow A=\dfrac{101}{2}\)