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\(a.\frac{35353535}{73737373}=\frac{35353535:1010101}{73737373:1010101}=\frac{35}{73}\)
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=(10-1)+(100-1)+(1000-1)+...........+(100.....0-1)
=(10+100+1000+......+1000.....0)-1-1-1-1-1-1-1-........-1
=10x(1+10+100+....+100........0)-1-1-1-.......1
con lai tu giai nhe!
de ma!
mk tra loi nhung ko bit co dung hk
D=9+99+999+...+9999...9(50 chu so 9)
D=(9+0)+(9+900)+.....(9+999.....0)
D=9.(0+100+...+999...0)
mk van chua tinh ra duoc quy luat cua no
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b: \(\dfrac{121212}{424242}=\dfrac{12}{42}=\dfrac{2}{7}\)
c: \(\dfrac{187187187}{221221221}=\dfrac{187}{221}=\dfrac{11}{13}\)
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\(M=3^0+3^1+3^2+...+3^{49}+3^{50}\)
\(3M=3^1+3^2+3^3+...+3^{50}+3^{51}\)
\(3M-M=3^{31}-1\)
\(2M=3^{4.7+3}-1\)
\(2M=81^7.27-1\)
\(2M=\overline{...1}.27-1\)
\(2M=\overline{...7}-1=\overline{...6}\)
\(M=\overline{...3}\Rightarrow M\)không phải số chính phương
Ta có công thức sau: \(k+kk+kkk+...+kkkk....k\)(n chữ số k)
\(=\frac{k}{9}\left(\frac{10^{n+1}-10}{9}-n\right)\)
\(A=\left[\frac{3}{9}.\left(\frac{10^{50+1}-10}{9}-50\right)\right].\left[\frac{9}{9}.\left(\frac{10^{50+1}-10}{9}-50\right)\right]\)
A=4,115226337 x \(10^{99}\)
A=33...3 . 999...9
=33..3 (100...0-1)
(50 số 0)
=33...3000...0-33..3
=333..3266..67
↓
(49 số 3;49 số 6)