\(H=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)\cdot\cdot\cdot\cdot\cdot\left(1-\frac{1}{100}\right)\)
\(\Leftrightarrow H=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\cdot\cdot\cdot\cdot\frac{99}{100}\)
\(\Leftrightarrow H=\frac{1.2.3.4.....99}{2.3.4.5.....100}\)
\(\Leftrightarrow H=\frac{1}{100}\)
\(H=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}...\frac{99}{100}\)
\(H=\frac{1.2.3.4...99}{2.3.4.5...100}\)
\(H=\frac{1}{100}\)
Vậy \(H=\frac{1}{100}.\)
\(H=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.....\frac{99}{100}\)
\(H=\frac{1.2.3.4.....99}{2.3.4.5.....100}\)
\(H=\frac{1}{100}\)
\(H=\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot\left(1-\frac{1}{5}\right)....\left(1-\frac{1}{100}\right)\)
\(H=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot...\cdot\frac{99}{100}\)
\(H=\frac{\left(1\cdot2\cdot3...99\right)}{\left(2\cdot3\cdot4...100\right)}\)
\(H=\frac{1}{100}\)
\(H=\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot\left(1-\frac{1}{5}\right)\cdot...\cdot\left(1-\frac{1}{100}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot...\cdot\frac{99}{100}\)
\(=\frac{1}{100}\)
Vậy \(H=\frac{1}{100}\)
H=\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot....\cdot\frac{99}{100}\)
H=\(\frac{1\cdot2\cdot3\cdot4\cdot....\cdot99}{2\cdot3\cdot4\cdot5\cdot....100}\)
H=\(\frac{1}{100}\)
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