Question

[Lạc Dao Dao]

H=\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).\left(1-\frac{1}{5}\right).....\left(1-\frac{1}{100}\right)\)

AI NHANH MIK TICK CHO

Answer 1

[Wall HaiAnh]

\(H=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)\cdot\cdot\cdot\cdot\cdot\left(1-\frac{1}{100}\right)\)

\(\Leftrightarrow H=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\cdot\cdot\cdot\cdot\frac{99}{100}\)

\(\Leftrightarrow H=\frac{1.2.3.4.....99}{2.3.4.5.....100}\)

\(\Leftrightarrow H=\frac{1}{100}\)

Answer 2

[Duc Loi]

\(H=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}...\frac{99}{100}\)

\(H=\frac{1.2.3.4...99}{2.3.4.5...100}\)

\(H=\frac{1}{100}\)

Vậy \(H=\frac{1}{100}.\)