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A= \(\dfrac{10.11.\left(1+5.5+7.7\right)}{11.12.\left(1+5.5+7.7\right)}=\dfrac{10}{12}=\dfrac{5}{6}\)
\(B=\dfrac{2^{19}\cdot27^3+15.4^9\cdot9^4}{6^9+2^{10}\cdot3^{10}}\)
\(\Rightarrow B=\dfrac{2^{19}\cdot\left(3^3\right)^3+3\cdot5\cdot4^9\cdot\left(3^2\right)^4}{2^3\cdot3^3+\left(2\cdot3\right)^{10}}\)
\(\Rightarrow B=\dfrac{2^{19}\cdot3^9+3\cdot5\cdot4^9\cdot3^8}{\left(2\cdot3\right)^3+\left(2\cdot3\right)^{10}}\)
\(\Rightarrow B=\dfrac{2^{19}\cdot3^9+5\cdot\left(2^2\right)^9\cdot3^9}{\left(2\cdot3\right)^{13}}\)
\(\Rightarrow B=\dfrac{2^{19}\cdot3^9+5\cdot2^{18}\cdot3^9}{2^{13}\cdot3^{13}}\)
\(\Rightarrow B=\dfrac{2\cdot\left(2^{18}\cdot3^9\right)+5\cdot\left(2^{18}\cdot3^9\right)}{2^{13}\cdot3^{13}}\)
\(\Rightarrow B=\dfrac{\left(2^{18}\cdot3^9\right)\cdot\left(2+5\right)}{2^{13}\cdot3^{13}}\)
\(\Rightarrow B=\dfrac{2^{18}\cdot3^9\cdot7}{2^{13}\cdot3^{13}}=\dfrac{2^{13}\cdot2^5\cdot3^9\cdot7}{2^{13}\cdot3^9\cdot3^4}\)
\(\Rightarrow B=\dfrac{2^5\cdot7}{3^4}\)
\(\frac{2^{19}\times27^3+15\times4^9\times9^4}{6^9\times2^{10}+12^{10}}\)
\(=\frac{2^{19}\times\left(3^3\right)^3+5\times3\times\left(2^2\right)^9\times\left(3^2\right)^4}{\left(2\times3\right)^9\times2^{10}+\left(3\times4\right)^{10}}\)
\(=\frac{2^{19}\times3^9+3\times5\times2^{18}\times3^8}{3^9\times2^9\times2^{10}+3^{10}\times4^{10}}\)
\(=\frac{2^{19}\times3^9+5\times2^{18}\times3^9}{3^9\times2^{19}+3^{10}\times\left(2^2\right)^{10}}\)
\(=\frac{2^{18}\times3^9\times\left(2+5\right)}{3^9\times2^{19}+3^{10}\times2^{20}}\)
\(=\frac{2^{18}\times3^9\times7}{2^{19}\times3^9\times\left(1+3\times2\right)}\)
\(=\frac{7}{2\times\left(1+6\right)}\)
\(=\frac{7}{2\times7}\)
\(=\frac{1}{2}\)
A = 2^19.27^3+15.4^9.9^4 / 6^9.2^10+12^10
= 2^19.3^9 + 5.2^18.3^9 / 3^9.2^19 + 2^20.3^10
= 2^18.3^9 ( 2 + 5 ) / 2^19.3^9.(1 + 2.3)
= (2 + 5) / 2(1 + 6)
= 7 / 2.7
= 1/2
A=2^19.3^9+3.5.2^18.3^8/3^9.2^9.2^10+3^10.2^20.
A=2^18.3^9.2+3^9.2^18.5/3^9.2^18.2+3^9.
A=3^9.2^18.(2+5)/3^9.2^18.(2+3.2^2).
A=7/14.
A=1/2.
\(=\dfrac{2^{19}\cdot3^9+2^{18}\cdot3^9\cdot5}{2^{19}\cdot3^9+2^{20}\cdot3^{10}}=\dfrac{2^{18}\cdot3^9\cdot\left(2+5\right)}{2^{19}\cdot3^9\cdot7}=\dfrac{1}{2}\)
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)
\(=\frac{2^{19}.3^9+2^{18}.3^9.5}{2^{19}.3^9+2^{19}.2.3^9.3}\)
\(=\frac{2^{18}.3^9.\left(2+5\right)}{2^{19}.3^9.\left(1+6\right)}\)
\(=\frac{7}{2.7}\)
\(=\frac{1}{2}\)
\(C=\frac{2^{19}.27^3-15.4^9.9^4}{6^9.2^{10}-12^{10}}\)
\(C=\frac{2^{19}.\left(3^3\right)^3-3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}-\left(3.2^2\right)^{10}}\)
\(C=\frac{2^{19}.3^9-3.5.2^{18}.3^8}{2^9.3^9.2^{10}-3^{10}.2^{20}}\)
\(C=\frac{2^{19}.3^9-3^9.2^{18}.5}{2^{19}.3^9-3^{10}.2^{20}}\)
\(C=\frac{2^{18}.3^9\left(2-5\right)}{2^{18}.3^9\left(2-3.2^2\right)}\)
\(C=\frac{-3}{-10}=\frac{3}{10}\)
N=1/2+1/22+...+1/210
2N=1+1/2+...+1/29
2N-N=1-1/210=1-1/1024=1023/1024
Giải:
N=1/2+1/22+1/23+...+1/29+1/210
2N=1+1/2+1/22+...+1/28+1/29
2N-N=(1+1/2+1/22+...+1/28+1/29)-(1/2+1/22+1/23+...+1/29+1/210)
N=1-1/210=1023/1024
Chúc bạn học tốt!
\(\dfrac{2^{19}.27^3+15.4^9.9^4}{9^4.4^{10}.12^{10}}\)
\(=\dfrac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(3^2\right)^4.\left(2^2\right)^{10}.\left(2^2.3\right)^{10}}\)
\(=\dfrac{2^{19}.3^9+3.5.2^{18}.3^8}{3^8.2^{20}.2^{20}.3^{10}}\)
\(=\dfrac{2^{19}.3^9+3^9.5.2^{18}}{3^{18}.2^{40}}\)
\(=\dfrac{2^{18}.3^9.\left(2+5\right)}{3^{18}.2^{40}}\)
\(=\dfrac{7}{3^9.2^{22}}\)
2 19 . 2 7 3 + 15. 4 9 . 9 4 9 4 . 4 10 + 1 2 10 9 4 .4 10 +12 10
2 19 .27 3 +15.4 9 .9 42 19 .( 2 7 3 + 27 3 ) + 15.4 9 .( 9 4 9 4 + 9 4 ) + 1 2 10 9 4 .4 10 +12 10
= 2 19 .100 + 15.4 9 . 94 + 1 2 10 9 4 .4 10 +12 10
= 2000 + 1410 + 1 2 10 9 4 .4 10 +12 10
= 2000 + 1410 + 2 10 9 + 12 10
= 2000+1412+123424