A = 5^5 +5^4 - 8.5^3
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
b) Ta có: \(B=\dfrac{7}{8}\cdot\dfrac{4}{9}+\dfrac{7}{8}\cdot\dfrac{5}{9}\)
\(=\dfrac{7}{8}\left(\dfrac{4}{9}+\dfrac{5}{9}\right)\)
\(=\dfrac{7}{8}\cdot1=\dfrac{7}{8}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=5^5+5^4-8.5^3=5^3\left(5^2+5-8\right)\)
\(=5^3.22=5^3.2.11\)\(⋮\)\(11\)
Vậy A chia hết cho 11
Ta có : A = 55 + 54 - 8 .53
= 53.(52 + 5 - 8)
= 53. 22
Vì 22 = 2 . 11 \(⋮\)11 => 53 . 22 \(⋮\)11
Vậy A \(⋮\)11
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=5^5+5^4-8.5^3\)
\(A=5^5+5^4-2^3.5^3\)
\(A=5^5+5^4-10^3\)
\(A=3750-1000\)
\(A=2750\)chia hết \(11\) ( vì ( 2 + 5 ) - ( 7 + 0 ) = 0 chia hết 11 )
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=5^5+5^4-8.5^3\)
\(A=5^3.\left(5^2+5-8\right)\)
\(A=5^3.22\)
\(A=5^3.2.11⋮11\)
Vay A chia het cho 11
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=5^5+5^4-8.5^3\)
\(A=5^3.\left(5^2+5-8\right)\)
\(A=5^3.22\)
\(A=5^3.2.11⋮11\)
Vậy \(A=5^5+5^4-8.5^3\)chia hết cho 11
Thực hiện phép tính
a. 8.5+73+4×3×5
B.8.3-(2018+8)÷3
C.(1024×18-1024×7+1024×5) ÷ 4096
D. 2+5+8+11+...+98
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Đặt \(C=\dfrac{1}{5}+\dfrac{1}{5^2}+...+\dfrac{1}{5^{100}}\)
\(\Rightarrow5C=1+\dfrac{1}{5}+\dfrac{1}{5^2}+...+\dfrac{1}{5^{99}}\)
\(\Rightarrow5C-C=1-\dfrac{1}{5^{100}}\Rightarrow4C=1-\dfrac{1}{5^{100}}\Rightarrow C=\dfrac{1-\dfrac{1}{5^{100}}}{4}\)
\(\Rightarrow A=8.5^{100}.\dfrac{1-\dfrac{1}{5^{100}}}{4}+1=2.\left(5^{100}-1\right)+1=2.5^{100}-2+1=2.5^{100}-1\)
b)\(B=\dfrac{4}{3}-\dfrac{4}{3^2}+...-\dfrac{4}{3^{100}}\)
\(B=4.\left(\dfrac{1}{3}-\dfrac{1}{3^2}+...-\dfrac{1}{3^{100}}\right)\)
Đặt \(\left(\dfrac{1}{3}-\dfrac{1}{3^2}+...-\dfrac{1}{3^{100}}\right)=D\)
\(\Rightarrow3D=1-\dfrac{1}{3}+...-\dfrac{1}{3^{99}}\)
\(\Rightarrow3D+D=1-\dfrac{1}{3^{100}}\)
\(\Rightarrow D=\dfrac{1-\dfrac{1}{3^{100}}}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Ta có: \(\left(8\cdot5^7+5^6-5^5\right):5^5\)
\(=8\cdot5^2+5-1\)
\(=200+4=204\)
b: Ta có: \(\left(9^{30}-27^{19}\right):3^{57}+\left(125^9-25^{12}\right):5^{24}\)
\(=3^{60}:3^{57}-3^{57}:3^{57}+5^{27}:5^{24}-5^{24}:5^{24}\)
\(=27-1+125-1\)
=150
a. (8,57 - 55 + 56) : 55
= (8,57 : 55) - (55 : 55) + (56 : 55)
= 1,72 - 1 + 5
= 2,89 - 1 + 5
= 6,89
b. (930 - 2719) : 357 + (1259 - 2512) : 524
= (930 : 357) - (2719 : 357) + (1259 : 524) - (2512 : 524)
= 33 - 1 + 125 - 1
= 27 - 1 + 125 - 1
= 150
c. (1012 + 511 . 29 - 513 - 28) : 4 . 55 . 106
= (1012 + 2,5 , 1010 - 513 - 28) : 1,25 . 1010
= (1012 : 1,25 . 1010) + (2,5 . 1010 : 1,25 . 1010) - (513 : 1,25 . 1010) - (28 : 1,25 . 1010)
= 80 + 2 - \(\dfrac{25}{256}\) - \(\dfrac{1}{48828125}\)
= 81,90234373 \(\approx\) 82
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{4^5\cdot10\cdot5^6+25^5\cdot2^8}{2^8\cdot5^4+5^7\cdot5^2}\\ =\dfrac{\left(2^2\right)^5\cdot2\cdot5\cdot5^6+\left(5^2\right)^5\cdot2^8}{2^8\cdot5^4+5^7\cdot5^2}\\ =\dfrac{2^{10}\cdot2\cdot5\cdot5^6+5^{10}\cdot2^8}{2^8\cdot5^4+5^7\cdot5^2}\\ =\dfrac{2^{11}\cdot5^7+5^{10}\cdot2^8}{2^8\cdot5^4+5^7\cdot5^2}\\ =\dfrac{2^8\cdot5^7\left(2^3+5^3\right)}{2^5\cdot5^4\left(2^3+5^3\right)}\\ =\dfrac{2^8\cdot5^7}{2^5\cdot5^4}\\ =2^3\cdot5^3\\ =8\cdot125\\ =1000\)
\(A=3125+625-8.125\)
\(A=\left(3125+625\right)-1000\)
\(A=3750-1000\)
\(A=2750\)