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Lê Vũ Thu Hà đã đăng 1 câu hỏi trên OLM
2019-1-13

tính tổng : A = 1 + \(\frac{1}{6}\)\(\frac{1}{12}\)\(\frac{1}{20}\)\(\frac{1}{30}\)\(\frac{1}{42}\)+ ........ + \(\frac{1}{90}\)\(\frac{1}{110}\)

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\(A=1+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}\)

\(=1+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)

\(=1+\frac{1}{2}-\frac{1}{11}=\frac{31}{22}\)

1Trả lời

\(A=1+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{90}+\frac{1}{110}\)

\(A=1+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}\)

\(A=1+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)

\(A=1+\frac{1}{2}-\frac{1}{11}\)

\(A=\frac{31}{22}\)

Vậy \(A=\frac{31}{22}\)

Trả lời
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