\(E=3-3^2+3^3-3^4+.....+3^{119}\)
\(3E=3\left(3-3^2+3^3-3^4+.....+3^{119}\right)\)
\(3E=3^2-3^3+3^4-3^5+.......+3^{120}\)
\(3E+E=\left(3^2-3^3+3^4-3^5+.....+3^{120}\right)+\left(3-3^2+3^3-3^4+.....+3^{119}\right)\)
\(3E+E=3-3^{120}\)
\(E=\dfrac{3-3^{120}}{4}\)
Tìm các số nguyên x, y:
a) \(\left|x-2\right|.y+\left|x-2\right|-17=0\)
b) \(3\left|x-5\right|-4=\left|1-3^2\right|\)
c) 8B - 7 = (-7)x biết B = 7 - 72 + 73 - 74 + ... +7119 - 7120 (\(x\in N\))
d) 2(x+3) = 3(1-x) - 2
e) \(70⋮\left(x-3\right);98\left(x-3\right)\) và x > 8
Cho E= 1/3+2/3^2+3/3^3+...+100/3^100. Chứng minh rằng: E<3/4
Bài 1: Chứng minh:
\(1+3+3^2+...+3^{119}\)chia hết cho 13
Bài 1 : Tính
a) 22 + 23 + 24 + ... + 2119
b) 2 + 22 + 23 + 24 + ... + 2101
Cho E\(=\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{2016}{3^{2016}}\)Chung minh E<\(\dfrac{3}{4}\)
Tính:
D=|-347|+(-40)+3150+(-307)
R =|-129|-119+|2-31|
Q= 100+98+96+...+4+2-97-95-...-3-1
tính giá trị biểu thức
a,A=52+53
b,B=42+43
c,C=25+33+21
d,D=13+23+33
e,E=631
g,K=11.322.37-915:(2.314)2
a) 52.49+48.38-52.20-48.11
b)2.54.12+4.6.68-3.8.22
c)24+31.24.64+24.8
d)19:3+28:3+13:3
e)32.15-{[(102.15-15.90)-43.2)
bài 2: tìm xϵN
a)32<2x<128
b)(x+1)2.3245:43-20
c)92-3(x-3) bằng 157:156
d)3x.310 bằng 317
e)81.3x+1 bằng 315
Thu gọn:
A = \(\dfrac{2^4.3^3+2^3.3^4}{2^5.3^3-2^4.3^2}\) D = \(\dfrac{\left(\dfrac{1}{2}-\dfrac{1}{3}\right).\left(\dfrac{2}{3}-\dfrac{3}{4}\right)}{\left(\dfrac{1}{2}+\dfrac{1}{3}\right).\left(\dfrac{2}{3}+\dfrac{3}{4}\right)}\)
B = \(\dfrac{2^3-3^4-2^4.3^3}{2^5.3^4-2^6.3^3}\) E = \(\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{3}{4}\right).\left(\dfrac{2}{3}-\dfrac{3}{4}+\dfrac{5}{6}\right)\)
C = \(\dfrac{\dfrac{1}{2}-\dfrac{1}{2}:\dfrac{3}{4}-\dfrac{3}{4}}{\dfrac{2}{3}-\dfrac{2}{3}:\dfrac{5}{6}-\dfrac{5}{6}}\)
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