A = 3+ 3/5+ 3/25+ 3/125+ 3/625

A = 3/1+ 3/5+ 3/25+ 3/125+ 3/625

A = 1875/625 + 375/625 + 75/625 + 15/625 + 3/625

A = 3 + 0,6 + 0,12 + 0,024 + 0,0048

A = 3,6 + 0,12 + 0,024 + 0,0048

A = 3,72 + 0,024 + 0,0048

A = 3,744 + 0,0048

A = 3,7488

       A =     3 + \(\dfrac{3}{5}\) + \(\dfrac{3}{25}\) + \(\dfrac{3}{125}\) + \(\dfrac{3}{625}\)

5\(\times\)A =   15 +  3 +   \(\dfrac{3}{5}\)  +  \(\dfrac{3}{25}\)  + \(\dfrac{3}{125}\)

5 \(\times\) A - A = 15 + 3 + \(\dfrac{3}{5}\) + \(\dfrac{3}{25}\) + \(\dfrac{3}{125}\) - (3 + \(\dfrac{3}{5}\) + \(\dfrac{3}{25}\) + \(\dfrac{3}{125}\) + \(\dfrac{3}{625}\))

4 \(\times\) A     = 15 + 3 + \(\dfrac{3}{5}\) + \(\dfrac{3}{25}\) + \(\dfrac{3}{125}\) - 3   - \(\dfrac{3}{5}\) - \(\dfrac{3}{25}\) - \(\dfrac{3}{125}\) - \(\dfrac{3}{165}\)

4  \(\times\) A =  (15 - \(\dfrac{3}{625}\)) + (3 - 3) + (\(\dfrac{3}{5}\) - \(\dfrac{3}{5}\)) + (\(\dfrac{3}{25}-\dfrac{3}{25}\)) + (\(\dfrac{3}{125}\)-\(\dfrac{3}{125}\))

4 \(\times\) A =   \(\dfrac{9372}{625}\)

       A = \(\dfrac{9372}{625}\) : 4

       A = \(\dfrac{2343}{625}\)

cho mẫu chung là 625 rồi tự quy đồng lên

=3\(\div\)(1+5+125+625)

=3\(\div\)756

=\(\frac{1}{252}\)

3+3/5+3/25+3/125+3/625= 3/625x(625+125+25+5+1)= 3x781/625=2343/625

chu y: vi 3=3x625/625 

3/5=3x125/125x5=3x125/625

3/25=3x25/25x25=3x25/625

3/125=3x5/125x5=3x5/625

3/625=3x1/625

cộng các kết quả trên và đặt 3/625 làm nhân từ chúng ta có kết quả như trên.

Đặt A=3+3/5+3/25+3/125+3/625=3/5+3/5^1+3/5^2+3/5^3+3/5^4

5A=15+3+3/5^1+3/5^2+3/5^3

5A-A=(15+3+3/5^1+3/5^2+3/5^3)-(3+3/5^1+3/5^2+3/5^3+3/5^4)

4A=15-3/625=9372/625

A=2343/625

cảm ơn nhìu

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 : \(3+\frac{3}{5}+\frac{3}{25}+\frac{3}{125}+\frac{3}{625}\)​​

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

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

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

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

thank