3+3/5+3/25+3/125+3/625
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DT
0
22 tháng 10 2019
3 + 3/5 + 3/25 + 3/125 + 3/625
= 1875/625 + 375/625 + 75/625 + 15/625 + 3/625
= 2250/625 + 90/625 + 3/625
= 2340/625 + 3/625
= 2343/625
VT
1 tháng 4 2015
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.
30 tháng 5 2018
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
7 tháng 7 2017
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 : \(3+\frac{3}{5}+\frac{3}{25}+\frac{3}{125}+\frac{3}{625}\)
\(=625\times\frac{3}{625}+125\times\frac{3}{625}+25\times\frac{3}{625}+5\times\frac{3}{625}+\frac{3}{625}\)
\(=\frac{3}{625}\left(625+125+25+5+1\right)\)
\(=\frac{3}{625}\times781\)
\(=\frac{2343}{625}\)
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 = \(\dfrac{2343}{625}\)