Question

[võ minh anh]

1/1+2+1/1+2+3+1/1+2+3+4.......+1/1=2+3+4+5+6+7+8+9+10

tính nhanh

Answer 1

[Luis Suárez]

Đặt A = \(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+10}\)

\(A=\frac{1}{\frac{2.3}{2}}+\frac{1}{\frac{3.4}{2}}+...+\frac{1}{\frac{10.11}{2}}\)

\(A=\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{10.11}\)

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

\(A=2.\left(\frac{1}{2}-\frac{1}{11}\right)\)

\(A=2\cdot\frac{9}{22}=\frac{9}{11}\)

Vậy A = \(\frac{9}{11}\)

Answer 2

[Lê Đức Thịnh]

Trả lời:

\(\frac{9}{11}\)nha

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