Question

Tìm gía trị của biểu thức sau:\(\frac{1}{1.3}\).\(\frac{1}{3.5}\).\(\frac{1}{5.6}\).....\(\frac{1}{99.100}\)

Answer 1

\(\frac{1}{1.3}.\frac{1}{3.5}.\frac{1}{5.6}.....\frac{1}{99.100}\)

\(=\frac{1}{1}.\left(\frac{1}{3.3}\right).\left(\frac{1}{5.5}\right).\left(\frac{1}{6.6}\right).....\left(\frac{1}{99.99}\right).\frac{1}{100}\)

\(=\frac{1}{1}.1.1.1.....1.\frac{1}{100}\)

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

 

Answer 2

\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{98}-\frac{1}{100}\right)\)\(=\frac{1}{2}.\left(1-\frac{1}{100}\right)=\frac{1}{2}.\frac{99}{100}=\frac{99}{200}\)