Question

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Tính nhanh:3+3/5+3/25+3/125+3/625

Answer 1

Ta thấy: \(3=3\times\frac{625}{625}=625\times\frac{3}{625}\)

\(\frac{3}{5}=\frac{3}{5}\times\frac{125}{125}=\frac{3\times125}{625}=125\times\frac{3}{625}\)

\(\frac{3}{25}=\frac{3}{25}\times\frac{25}{25}=\frac{3\times25}{625}=25\times\frac{3}{625}\)

\(\frac{3}{125}=\frac{3}{125}\times\frac{5}{5}=\frac{3\times5}{625}=5\times\frac{3}{625}\)

Từ đó, suy ra : \(3+\frac{3}{5}+\frac{3}{25}+\frac{3}{125}+\frac{3}{625}\)​​

 \(=625\times\frac{3}{625}+125\times\frac{3}{625}+25\times\frac{3}{625}+5\times\frac{3}{625}+\frac{3}{625}\)

\(=\frac{3}{625}\left(625+125+25+5+1\right)\)

\(=\frac{3}{625}\times781\)

\(=\frac{2343}{625}\)

Answer 2

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