Question

[Liên Quân Mobile]

Tính nhanh :

A = 1/3 + 1/6 + 1/10 + ... + 1/4950

Answer 1

[黎高梅英]

A = \(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{1}{4950}\)

A = \(2.\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{9900}\right)\)

A = \(2.\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)

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

A = \(1-\dfrac{1}{50}\)

A = \(\dfrac{49}{50}\)

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Answer 2

[Phương Trâm]

\(A=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{1}{4950}\)

\(\Rightarrow2A=\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{9900}\)

\(\Rightarrow2A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

\(\Rightarrow2A=\dfrac{1}{2}-\dfrac{1}{100}\)

\(\Rightarrow A=1-\dfrac{1}{50}\)

\(\Rightarrow A=\dfrac{49}{50}\)