Question

A=1/2.3+1/3.4+...+1/99.100

Answer 1

\(A=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

ta có: \(\frac{1}{2.3}=\frac{1}{2}-\frac{1}{3}\)

\(\frac{1}{3.4}=\frac{1}{3}-\frac{1}{4}\)

...

\(\frac{1}{99.100}=\frac{1}{99}-\frac{1}{100}\)

Vậy \(A=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

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

\(=\frac{1}{2}-\frac{1}{100}\)

\(=\frac{50}{100}-\frac{1}{100}=\frac{49}{100}\)

vậy A = 49/100