Question

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Tính hợp lý:

\(C=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{98.99.100}\)

Answer 1

[Nguyen My Van]

\(2C=\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+\dfrac{2}{98.99.100}\)

\(=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{98.99}-\dfrac{1}{99.100}\)

\(=\dfrac{1}{1.2}-\dfrac{1}{99.100}=\dfrac{50.99-1}{100.99}=\dfrac{4949}{9900}\)

Answer 2

[2611]

`A=1/[1.2.3]+1/[2.3.4]+....+1/[98.99.100]`

`A=1/2.(2/[1.2.3]+2/[2.3.4]+....+2/[98.99.100])`

`A=1/2.(1/[1.2]-1/[2.3]+1/[2.3]-1/[3.4]+....+1/[98.99]-1/[99.100])`

`A=1/2.(1/[1.2]-1/[99.100])`

`A=1/2.(1/2-1/9900)`

`A=1/2.(4950/9900-1/9900)`

`A=1/2 . 4949/9900`

`A=4949/19800`