Question

Tính giá trị của biểu thức sau:

1/1 * 2 + 1/2 * 3 + .................... + 1/98 * 99 + 1/99 * 100

Answer 1

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

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

\(=\frac{1}{1}-\frac{1}{100}=\frac{99}{100}\)

Answer 2

ĐẶT : A= \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}\)\(\)
 

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

= \(1-\frac{1}{99}=\frac{98}{99}\)

Answer 3

Gọi tổng đó là S 

TA có : S = \(\frac{1}{1.2}+\frac{1}{2.3}+......\frac{1}{98.99}+\frac{1}{99.100}\)

S = \(\frac{1}{1.2}-\frac{1}{99.100}=\frac{1}{2}-\frac{1}{9900}=\frac{4949}{9900}\)

Vậy S = \(\frac{4949}{9900}\)