Question

A=\(\dfrac{2}{1.2}\)+\(\dfrac{2}{2.3}\)+\(\dfrac{2}{3.4}\)+...+\(\dfrac{2}{99.100}\)

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Answer 1

Gợi ý :  ^''Cần Cù Thì Bù Siêng Năng '' nhé :)

Answer 2

\(A=\dfrac{2}{1.2}+\dfrac{2}{2.3}+\dfrac{2}{3.4}+...+\dfrac{2}{99.100}\)

\(A=2\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\right)\)

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

\(A=2\left(1-\dfrac{1}{100}\right)\)

\(A=2.\dfrac{99}{100}\)

\(A=\dfrac{99}{50}\)

Answer 3

\(=>A=2.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\right)\)

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

\(=>A=2.\left(1-\dfrac{1}{100}\right)\)

\(=>A=2.\dfrac{99}{100}\)

\(=>A=\dfrac{99}{50}\)