\(\dfrac{3}{1^2.2^2}+\dfrac{5}{2^2.3^2}+...+\dfrac{19}{9^{10}.10^2}\)
\(=\dfrac{1}{1^2}-\dfrac{1}{2^2}+\dfrac{1}{2^2}-\dfrac{1}{3^2}+...+\dfrac{1}{9^{10}}-\dfrac{1}{10^2}\)
\(=1-\dfrac{1}{10^2}< 1\)
\(\Rightarrowđpcm\)
Chứng tỏ:
\(\dfrac{1}{3} + \dfrac{1}{3^2} +...+ \dfrac{1}{3^{99}} < \dfrac{1}{2}\)
\(\dfrac{3}{1^2.2^2} + \dfrac{5}{2^2.3^2} + ...+ \dfrac{19}{9^2.10^2}<1 \)
Bài 8: Viết các biểu thức sau đây dưới dạng a^n (a e Q; n e N*)
a, 9. 3^5. 1/81 ; b, 8.2^4: (2^3.1/16) ; c, 3^2.3^5:1/27 ; d, 125.5^2.1/625
Bài 12: Tính:
a) (-0,1)^2.(-0,1)^3 ; b) 125^2 : 25^3 ; c) (7^3)^2 : (7^2)^3 ; d) (-2)^3+2^2+(-1)^20+(-2)^0 ; e) 2^4+8.[(-3)^2 : 1/2]^0-2^-2.4+(-2)^-2
B1:Tính
a)(-2/3+3/7):4/5+(-1/3+4/7):4/5
b)5/9:(1/11-5/22)+5/9:(1/15-2/3)
c)4^2.4^3/4^10
d)(0,6)^5/(0,2)^6
e)2^7.9^3/6^5.8^2
g)6^3+3.6^2+3^3/-13
h)(3/7+1/2)^2
i)(3/4-5/6)^2
k)5^4.20^44/25^5.4^5
l)(-10/3)^5.(-6/5)^4
f)(1+2/3-1/4).(4/5-3/4)^2
m)2:(1/2-2/3)^3
n)9.9.(-1/3)^3+1/3
y)(4.2^5):(2^3.1/16)
Bài 1:
\(\frac{8^{18}+1}{8^{19}+1}\)
Bài 2:
a) Chứng minh: \(9^{1945}-2^{1930}\) chia hết cho 5
b) Chứng minh: \(4^{2010}+2^{2014}\) chia hết cho 10
Tính:
a) S=1.2+2.3+3.4+...+99.100
b) B=\(\dfrac{49^{24}.125^{17}.2^8-5^{30}.7^{49}.4^5}{5^{29}.16^2.7^{48}}\)
c) C=\(\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}\right).3^5+\left(\dfrac{1}{3^5}+\dfrac{1}{3^6}+\dfrac{1}{3^7}+\dfrac{1}{3^8}\right).3^9+...+\left(\dfrac{1}{3^{97}}+\dfrac{1}{3^{98}}+\dfrac{1}{3^{99}}+\dfrac{1}{3^{100}}\right).3^{101}\)
d) D= \(3-3^2+3^3-3^4+...+3^{2017}-3^{2018}\)
Viết các biểu thức số sau dưới dạng \(a^n,\left(a\in\mathbb{Q},n\in\mathbb{N}\right)\) :
a) \(9.3^3.\dfrac{1}{81}.3^2\)
b) \(4.2^5:\left(2^3.\dfrac{1}{16}\right)\)
c) \(3^2.2^5.\left(\dfrac{2}{3}\right)^2\)
d) \(\left(\dfrac{1}{3}\right)^2.\dfrac{1}{3}.9^2\)
Chứng minh rằng: \(3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\)⋮ 6
Bài 4 : Tính giá trị các biểu thức :
a. A= 22 - (-32)3 + 4-2 .16-2.52 .
b. B= (23 : 1/2) . 1/2+3-2.9-7. (14/25)0+5 .
c. C= 2-3 + (52)3.5-3+4-3 . 16 -2.32-105. (24/51)0 .
d. D= (2-3.1/2-2).2/3+4-2.8-7.(17/23)0+19 .
2 / tìm tính
a/\(\dfrac{2^3.6^2}{3^2.4^2}\)=
b/\(\left(\dfrac{3}{2}\right)^{-2+}\dfrac{1}{3}.\left(\dfrac{3}{4}\right)^{-1}+0,\left(3\right)\)=
c/\(\left(\dfrac{5}{3}\right)^{-2}+\dfrac{-1}{5}-0,2\)=
