Question

so sánh

a: A=2^0+2^1+2^2+2^3+....+2^2010 và B=2^2011-1

b: A=2009.2011 và B=2010^2

c: A= 10^30 và B = 2^100

d; A= 333^444 và B= 444^333

e: A= 3^150 và B= 5^300

Answer 1

a , Ta có :

A = \(2^0+2+2^2+...+2^{2010}\)

=> 2A = \(2+2^2+...+2^{2010}+2^{2011}\)

=> A = 2A-A = \(2^{2011}-2^0=2^{2011}-1\)= B

Answer 2

b , Ta có A = 2009.2011=2009(2010+1)=2009.2010+2009

B = 2010² = 2010.2010=(2009+1)2010=2009.2010+2010

Vì 2010>2009 => 2009.2010+2009<2009.2010+2010 hay A<B

c , Ta có : A = \(10^{30}=\left(10^3\right)^{10}=1000^{10}\)

B = \(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

Vì 1024¹⁰ > 1000¹⁰ => A < B

Answer 3

\(A=2^0+2^1+2^2+2^3+....+2^{2010}\)

\(2A=2^1+2^2+2^3+2^4+.....+2^{2011}\)

\(2A-A=\left(2^1+2^2+2^3+2^4+.....+2^{2011}\right)-\left(2^0+2^1+2^2+2^3+....+2^{2010}\right)\)\(A=2^{2011}-2^0=2^{2011}-1\)

\(A=B=2^{2011}-1\)

\(A=2009.2011=2009.\left(2010+1\right)=2009.2010+2011\)

\(B=2010^2=2010.2010=2010\left(2009+1\right)=2010.2009+2010\)

\(A>B\)

\(A=10^{30}=\left(10^3\right)^{10}=1000^{10}\)

\(B=2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

\(A< B\)

\(A=333^{444}=\left(333^4\right)^{111}=\left(3^4.111^4\right)^{111}=\left(81.111^4\right)^{111}\)

\(B=444^{333}=\left(444^3\right)^{111}=\left(4^3.111^3\right)^{111}=\left(64.111^3\right)^{111}\)

\(A>B\)

\(A=3^{150}\)

\(B=5^{300}=\left(5^2\right)^{150}=25^{150}\)

\(A< B\)

Answer 4

so sanh a*b /a^2+b^2 va a^2+b^2/(a+b)^2