Question

[Kim Anh Le]

Tính bằng cách thuận tiện nhất:

1-1/5 × 1-1/6 × 1-1/7 × 1-1/8 × ...× 1-1/100.

Mọi người giúp với!!!!!!

Answer 1

[The Angry]

\(1-\frac{1}{5}\times1-\frac{1}{6}\times.....\times1-\frac{1}{100}\)

\(=\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}\times.....\times\frac{99}{100}\)

\(=\frac{4\times5\times....\times99}{5\times6\times...\times100}\)

\(=\frac{1}{25}\)

Answer 2

[FL.Han_]

Ta có: \(\left(1-\frac{1}{5}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{7}\right)\left(1-\frac{1}{8}\right)...\left(1-\frac{1}{100}\right)\)

\(=\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdot...\cdot\frac{98}{99}\cdot\frac{99}{100}\)

\(=\frac{4}{100}=\frac{1}{25}\)