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A2=2+2^2+2^3+...2^99+2^100+2^101
-
A=1+2+2^2+2^3+...2^100
A2-A=2^101-1
->A=2^101-1
a ,
\(x.x^2.x^3.x^4.x^5......x^{49}.x^{50}.x=x^{24.\left(1+49\right)+51}=x^{1251}\)
a) x . x2 . x3 . ... . x50
= x(1 + 2 + 3 + ... + 50)
= x1275
2 . A = 2 + 2^2 +....+2^2009
A = 2A -A = 2^2009-1
A<B
B- A = 1
\(7^2.49^3.7^7=7^2.\left(7^2\right)^3.7^7=7^2.7^6.7^7=7^{15}\)
\(3^5.9^4.27^2.81=3^5.\left(3^2\right)^4.\left(3^3\right)^2.3^4=3^5.3^8.3^6.3^4=3^{23}\)
a) \(7^2.49^3.7^7=7^2.7^6.7^7=7^{15}\)
b) \(3^5.9^4.27^2.81=3^5.3^8.3^6.3^4=3^{23}\)
\(a,81^3\cdot\frac{1}{9^2}:3^3=\left(9^2\right)^3\cdot\frac{1}{9^2}:3^3=9^6\cdot\frac{1}{9^2}\cdot\frac{1}{3^3}=\frac{9^6}{9^2}\cdot\frac{1}{3^3}=9^4\cdot\frac{1}{3^3}=\left(3^2\right)^4\cdot\frac{1}{3^3}=\frac{3^8}{3^3}=3^5\)
\(b,625^4:25^2=\left(5^4\right)^4:\left(5^2\right)^2=5^{16}:5^4=5^{12}\)
Bài 1
a) 34 + 35 + 36 + 37 = 34(1 + 3 + 32 + 33)\
b) a)A = 1 + 3 + 32 +......399 =(1 + 3 + 32 + 33 ) + ...+(396 + 397 + 398 + 399)
= (1 + 3 + 32 + 33 ) + .. +396(1 + 3 + 32 + 33 )
= 40 + ... + 396 . 40
= 40 (1 + 3 +...+ 396) chia hết cho 40
Bài 2
a)
+)A chia hết cho 6
\(A=5+5^2+5^3+...+5^{2004}\)
\(A=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{2003}+5^{2004}\right)\)
\(A=\left(5+5^2\right)+5^2\left(5+5^2\right)+...+5^{2002}\left(5+5^2\right)\)
\(A=30+5^2.30+...+5^{2002}.30\)
\(A=30\left(1+5^2+...+5^{2002}\right)\)chia hết cho 6
+)A chia hết cho 31
\(A=5+5^2+5^3+...+5^{2004}\)
\(A=\left(5+5^2+5^3\right)+\left(5^4+5^5+5^6\right)+...+\left(5^{2002}+5^{2003}+5^{2004}\right)\)
\(A=\left(5+5^2+5^3\right)+5^3\left(5+5^2+5^3\right)+...+5^{2001}\left(5+5^2+5^3\right)\)
\(A=155+5^3.155+...+5^{2001}.155\)
\(A=155\left(1+5^3+...+5^{2001}\right)\)chia hết cho 31
+) A chia hết cho 156
\(A=5+5^2+5^3+...+5^{2004}\)
\(A=\left(5+5^2+5^3+5^4\right)+\left(5^5+5^6+5^7+5^8\right)+...+\left(5^{2001}+5^{2002}+5^{2003}+5^{2004}\right)\)
\(A=\left(5+5^2+5^3+5^4\right)+5^4\left(5+5^2+5^3+5^4\right)+...+5^{2000}\left(5+5^2+5^3+5^4\right)\)
\(A=780+5^4.780+...+5^{2000}.780\)
\(A=780\left(1+5^4+...+5^{2000}\right)\)chia hết cho 156
b)B=165+2^15 chia hết cho 33
ta có 165 chia hết cho 33
mà 215 ko chia hết cho 33
vậy 165+2^15 không chia hết cho 33 hay B không chia hết cho 33.
a) M = 1 + 2 + 22 + 23 + ..... + 22019
= ( 1 + 2 + 4 ) + 23( 1 + 2 + 4 ) +.... + 22016 ( 1 + 2 + 4 )
= 7 ( 1 + 23 + 22016 ) chia hết cho 7 (đpcm)
b) M + 1 = 1 + 1 + 2 + 22 + 23 +... + 22019
= 4 + 22 + 2 3 + .....22019
= 2 x 22 + 23 + .... + 22019
= 2 x 23 + .... + 22019
= 2 x 2 2019
= 22020