Question

A 99/101 B 99/100 C 99/202 D 100/101 tính giá trị biểu thức : 1/3 + 1/6 + 1/10+ 1/15 +...... + 1/5050

Answer 1

\(\frac13+\frac16+\frac{1}{10}+\frac{1}{15}+\cdots+\frac{1}{5050}\)

\(=\frac26+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\cdots+\frac{2}{10100}\)

\(=2\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+\cdots+\frac{1}{100\times101}\right)\)

\(=2\times\left(\frac12-\frac13+\frac13-\frac14+\cdots+\frac{1}{100}-\frac{1}{101}\right)\)

\(=2\times\left(\frac12-\frac{1}{101}\right)=1-\frac{2}{101}=\frac{99}{101}\)

=>Chọn A