Question

2/1x2 + 2/2x3 + 2/3x4 +...+ 2/98x99 + 2/99x100

Tính: ????

x là: nhân

Answer 1

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

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

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

= \(2.\left(1-\frac{1}{100}\right)\)

= \(2.\frac{99}{100}\)

= \(\frac{99}{50}\)