Question

Tính [100-(1+1/2+1/3+...+1/100)]:(1/2+2/3+...+99/100)

Answer 1

\(100-\left(1+\frac12+\frac13+\cdots+\frac{1}{100}\right)\)

\(=100-1-\frac12-\frac13-\cdots-\frac{1}{100}\)

\(=99-\frac12-\frac13-\cdots-\frac{1}{100}\)

\(=\left(1-\frac12\right)+\left(1-\frac13\right)+\cdots+\left(1-\frac{1}{100}\right)\)

\(=\frac12+\frac23+\cdots+\frac{99}{100}\)

Do đó: \(\frac{100-\left(1+\frac12+\frac13+\cdots+\frac{1}{100}\right)}{\frac12+\frac23+\cdots+\frac{99}{100}}=1\)