Question

Tính giá trị các biểu thức

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

C=(1-1/2)(1-1/3)(1-1/4)...(1-1/1000)

Ai nhanh giúp mình,mình tích cho.

Answer 1

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

    = \(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{101}{100}\)

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

C = \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{1000}\right)\)

   \(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{999}{1000}\)

    \(=\frac{1.2.3...999}{2.3.4....1000}=\frac{1}{1000}\)