Question

Tính tổng S= 2/1.2 + 2/2.3 + 2/3.4 +............+ 2/98.99 + 2/99.100

Answer 1

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{98.99}+\frac{2}{99.100}\)

= \(2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\)

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

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

 =\(2.\frac{99}{100}\)

 =\(\frac{99}{50}\)