Question

So sánh: \(^{ }9^{87}va27^{58}\)\(3^{222}va2^{333}\)\(\left(2^2\right)^3va2^{2^3}^{ }\)\(2^{3^2}va2^{2^3}\)\(\left(-1\right)^{4^5}va\left(-1\right)^{5^4}\)\(4^{30}va3\cdot24^{10}\)​\(2^{101}va5^{39}\)\(3^{5n}va5^{3n}\)\(101^{15}va9^{29}\)\(3^{201}va2^{301}\)\(404^{600}va505^{450}\)a) Cho A = \(1+2+2^2+2^3+...+2^{10}\)so sánh A và \(2^{11}\)b) Cho B = \(2.2^2+3.2^3+4.2^4+5.2^5+...+10.2^{10}\)so sánh B và \(2^{14}\)

Answer 1

Bài làm 

Đặt a - b = x ; b - c = y ; c - a = z 

 => x + y + z = 0

 Ta có :

          \(N=\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)^2-2.\left(\frac{1}{xy}+\frac{1}{yz}+\frac{1}{xz}\right)=\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)^2-2.\left(\frac{x+y+z}{xyz}\right)\)

=>     \(N=\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)^2\)( Vì x + y + z = 0 )

Vậy ta có đpcm