Question

giải hộ mình nha

A=\(\frac{9}{1\cdot2}+\frac{9}{2\cdot3}+\frac{9}{3\cdot4}+....+\frac{9}{98\cdot99}+\frac{9}{99\cdot100}\)

cảm ơn nhiều ạ

Answer 1

A = 9(\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\))

A = 9(\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\))

A = 9(1 - \(\frac{1}{100}\))

A = 9.\(\frac{99}{100}\)=\(\frac{891}{100}\)=8,91

Vì \(\frac{1}{1.2}=\frac{1}{2}\)

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

Nên trong bài toán: \(\frac{1}{1.2}=\frac{1}{1}-\frac{1}{2}\)

Mấy cái kia cũng vậy nên bạn yên tâm nha!!!!

Answer 2

A : 9 = 1/1.2 + 1/2.3 + 1/3.4 + ..... + 1/98.99 + 1/99.100

A : 9 = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ..... + 1/98 - 1/99 + 1/99 - 1/100

A : 9 = 1 - 1/100

A : 9 = 100/100 - 1/100

A : 9 = 99/100

A = 9 . 99/100

A = 891/100 = 8,91 = 8 91/100