Question

[phạm quốc bảo]

tính

A=1+2/6+2/12+...+2/9702+2/9900

Answer 1

[Bùi Thế Hào]

\(A=1+\frac{2}{6}+\frac{2}{12}+...+\frac{2}{9702}+\frac{2}{9900}=1+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{98.99}+\frac{2}{99.100}\)

=> \(A=1+2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\)

\(A=1+2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)

\(A=1+2\left(\frac{1}{2}-\frac{1}{100}\right)=1+2.\frac{49}{100}=1+\frac{49}{50}=\frac{99}{50}\)

Đáp số: \(A=\frac{99}{50}\)

Answer 2

[phạm quốc bảo]

thanks bạn nha Bùi Thế Hào