Question

So Sánh

a)\(A=3^0+3^1+3^2+....+3^{2016}\) và \(B=3^{2017}\)

b)\(A=\frac{2^{2016}+1}{2^{2008}+1}\)và \(B=\frac{2^{2012}+1}{2^{2009}+1}\)

c)\(A=\frac{3^{123}+1}{3^{125}+1}\)và \(B=\frac{3^{122}}{3^{124}+1}\)

d)\(A=2^{30}+3^{20}+4^{30}\)và \(B=3.24^{10}\)

e)\(A=5^{84}\)và \(B=3^{126}\) và \(C=2^{108}\)

GIÚP MÌNH VỚI NHA!  ( ^ _ ^ )

Answer 1

\(A=1+3+3^2+3^3+...+3^{2016}\)

\(A=1+3\left(1+3^2+...+3^{2015}\right)\)

\(A=1+3\left(A-3^{2016}\right)\)

\(A=1+3A-3^{2017}\)

\(2A=3^{2017}-1\Rightarrow A=\frac{3^{2017}-1}{2}\)

\(A< B\)