Question

So sánh 2 phân số \(A=\frac{2^{2015}+1}{2^{2016}+1}\) và \(B=\frac{2^{2016}+1}{2^{2017}+1}\)

Answer 1

Ta có 2A= 2(2^2015 + 1)/ 2^2016 + 1 =  2^2016 +2 / 2^2016 +1 = 2^2016+1/2^2016+1 + 1/2^2016 +1= 1 + 1/2^2016 

2B= 2(  2^2016 + 1/ 2^2017+ 1) =  2^2017 +2 / 2^2017 +1 = 2^2017+1/2^2017+1 + 1/2^2017 +1 = 1 + 1/2^2017

Do 1/2^2016 > 1/2^2017 => 2A>2B => A>B

Answer 2

10.A=\(10.A=\frac{10.\left(2^{2015+1}\right)}{2^{2016}+1}=\frac{2^{2016+10}}{2^{2016}+1}=1+\frac{2016}{2^{2016}+1}\)

\(10.B=\frac{10.\left(2^{2016}+1\right)}{2^{2017}+1}=\frac{2^{2017}+10}{2^{2017}+1}=1+\frac{2016}{2^{2017}+1}\)

Ta có:\(\frac{2016}{2^{2016}+1}>\frac{2016}{2^{2017}+1}\)

Answer 3

\(A=\frac{2^{2015}+1}{2^{2016}+1}\)

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

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

\(B=\frac{2^{2016}+1}{2^{2017}+1}\)

\(2B=\frac{2^{2017}+1+1}{2^{2017}+1}\)

\(2B=1+\frac{1}{2^{2017}+1}\)

=> 2A > 2B

=> A>B

Answer 4

Cách làm của Nguyễn Tường Vi sai rồi