Question

[Go Eun Biii VIP]

T =  1/2 +1/6 +1/12 + 1/20 + 1/30 + ... + 1/9702 + 1/9900

Hãy tính T = tổng các bn nhé !

Answer 1

[Nguyễn Hoàng Hải Nam]

T = \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{98\cdot99}+\frac{1}{99\cdot100}=\)

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

T = \(\frac{1}{1}-\frac{1}{100}=\)

T = \(\frac{99}{100}\)