Question

[Trần Như]

Tính một cách hợp lý:

A = 2 x ( 1/1x2x3+ 1/2x3x4+ 1/3x4x5+ .... + 1/98x99x100 )

Answer 1

[Nam Nguyễn]

Giải:

Ta có:

\(A=2\left(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{98.99.100}\right).\)

\(A=\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+\dfrac{2}{3.4.5}+...+\dfrac{2}{98.99.100}.\)

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

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

\(A=0+0+...+0+\left(\dfrac{1}{1.2}-\dfrac{1}{99.100}\right).\)

\(A=\dfrac{1}{1.2}-\dfrac{1}{99.100}.\)

\(A=\dfrac{1}{2}-\dfrac{1}{9900}.\)

\(A=\dfrac{4950}{9900}-\dfrac{1}{9900}.\)

\(A=\dfrac{4949}{9900}.\)

Vậy \(A=\dfrac{4949}{9900}.\)

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Answer 2

[Nguyễn Minh Hoàng]

:P