Question

Tính

D=(1/2-1).(1/3-1).(1/4.1)...(1/50-1)

 

Answer 1

Lời giải:

\(D=(\frac{1}{2}-1)(\frac{1}{3}-1)(\frac{1}{4}-1)...(\frac{1}{50}-1)=\frac{1-2}{2}.\frac{1-3}{3}.\frac{1-4}{4}...\frac{1-50}{50}\)

\(=\frac{-1}{2}.\frac{-2}{3}.\frac{-3}{4}....\frac{-49}{50}=-\frac{1.2.3.4...49}{2.3.4...50}=\frac{-1}{50}\)