khó quá giải hộ đê :
9 mũ 9 + 9 mũ 10 ..... 9 mũ 20
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=1024.59049-1024.19683
=1024.(59049-19683)
=1024.39366
=40310784/=512.50049
=30233088
=10^6x(10^3+10^2+10)=10^6x1110=10^6x2x555 suy ra chia hết cho 555
\(\dfrac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^{29}\cdot9^{10}-7\cdot2^{29}\cdot27^6}\)
\(=\dfrac{5\cdot2^{30}\cdot3^{18}-2^2\cdot2^{27}\cdot3^{20}}{5\cdot2^{29}\cdot3^{20}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{29}\cdot3^{18}\left(5\cdot3^2-7\right)}\)
\(=\dfrac{10-9}{5\cdot9-7}=\dfrac{1}{38}\)
\(a=4^5.9^4-2.\dfrac{6^9}{2^{10}}.3^8+6^8.20\)
Đề là như vầy đúng ko bn?
a)\(\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}=\frac{-5}{9}\)
b)\(\frac{\left(-11\right)^5.13^7}{11^5.13^8}=-\frac{1}{13}\)
c)\(\frac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}=\frac{2^{10}.3^9\left(3-1\right)}{2^9.3^{10}}=2\)
d(\(\frac{5^{11}.7^{12}+5^{11}.7^{11}}{5^{12}.7^{12}+9.5^{11}.7^{11}}=\frac{5^{11}.7^{11}\left(7+1\right)}{5^{11}.7^{11}\left(35+9\right)}=\frac{1}{6}\)
I don't now
or no I don't
..................
sorry
Đặt: \(A=9^9+9^{10}+...+9^{20}\)
\(9A=9\cdot\left(9^9+9^{10}+...+9^{20}\right)\)
\(9A=9^{10}+9^{11}+...+9^{21}\)
\(9A-A=9^{10}+9^{11}+...+9^{21}-9^9-9^{10}-...-9^{20}\)
\(8A=9^{21}-9^9\)
\(A=\dfrac{9^{21}-9^9}{8}\)
Đặt $A=9^9+9^{10}+...+9^{20}$
$9\cdot A=9\cdot(9^9+9^{10}+...+9^{20})$
$9A=9^{10}+9^{11}+...+9^{21}$
$9A-A=(9^{10}+9^{11}+...+9^{21})-(9^9+9^{10}+...+9^{20})$
$8A=9^{21}-9^9$
$\Rightarrow A=\dfrac{9^{21}-9^9}{8}$