Question

Tính phép tính sau:

1/2+ 1/3+ 1/4+ .........+1/100

(Giải chi tiết giúp tôi, cảm ơn !)

Answer 1

Đặt :

\(A=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+....................+\dfrac{1}{100}\)

\(2A=1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+....................+\dfrac{1}{99}\)

\(\Rightarrow2A-A=\left(1+\dfrac{1}{2}+........+\dfrac{1}{99}\right)-\left(\dfrac{1}{2}+\dfrac{1}{3}+.................+\dfrac{1}{100}\right)\)

\(\Rightarrow A=1-\dfrac{1}{100}=\dfrac{99}{100}\)

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