Question

Tính nhanh:

B=(1+1/2)x(1+1/3)x(1+1/4)...x(1+1/99)

Giải giùm mình nha! Mai mình thi rồi!!!!!

Answer 1

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

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

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

\(\Rightarrow B=\frac{3.4.5...100}{2.3.4...99}\)

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

\(\Rightarrow B=50\)

Vậy \(B=50\)