Question

[Phuc Cầu]

A=9/1*2+9/2*3+9/3*4+...9/96*99+9/99*100

Answer 1

[ChaosKiz]

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

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

\(A=9-\dfrac{9}{100}\)

\(A=\dfrac{891}{100}\)

Answer 2

[Nguyễn Thanh Hằng]

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

\(\Rightarrow A=9\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+.................+\dfrac{1}{98.99}+\dfrac{1}{99.100}\right)\)

\(\Rightarrow A=9\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+..........+\dfrac{1}{98}-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{100}\right)\)

\(\Rightarrow A=9\left(1-\dfrac{1}{100}\right)\)

\(\Rightarrow A=9.\dfrac{99}{100}\)

\(\Rightarrow A=\dfrac{891}{100}\)