Question

[Đức Kiều Anh]

A=12/40+12/88+12/154+12/238+12/340

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Answer 1

[Tung Duong]

\(A=\frac{12}{40}+\frac{12}{88}+\frac{12}{154}+\frac{12}{238}+\frac{12}{340}\)

\(A=\frac{12}{5\times8}+\frac{12}{8\times11}+\frac{12}{11\times14}+\frac{12}{14\times17}+\frac{12}{17.20}\)

\(A=4\times\left(\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+\frac{3}{14\times17}+\frac{3}{17\times20}\right)\)

\(A=4\times\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\right)\)

\(A=4\times\left(\frac{1}{5}-\frac{1}{20}\right)\)

\(A=4\times\frac{3}{20}=\frac{12}{20}=\frac{3}{5}\)