Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
A = 152015+1/152016+1 < 152015+1+14/152016+1+14
= 152015+15/152016+15
= 15.(152014+1)/15.(152015+1)
= 152014+1/152015+1 = B
=> A<B
A = \(\frac{2015^{2016}+1}{2015^{2015}+1}=\frac{2015^{2015}+1}{2015^{2015}+1}+\frac{2015}{2015^{2015}+1}=1+\frac{2015}{2015^{2015}+1}\)
B = \(\frac{2014^{2015}+1}{2014^{2014}+1}=\frac{2014^{2014}+1}{2014^{2014}+1}+\frac{2014}{2014^{2014}+1}=1+\frac{2014}{2014^{2014}+1}\)
Rồi bạn tự so sánh nha
\(A=\frac{-7}{2016^{2015}}+\frac{-15}{2016^{2016}}=\frac{-7.2016}{2016^{2016}}+\frac{-15}{2016^{2016}}=\frac{-14127}{2016^{2016}}\)
\(B=\frac{-15}{2016^{2015}}+\frac{-7}{2016^{2016}}=\frac{-15.2016}{2016^{2016}}+\frac{-7}{2016^{2016}}=\frac{-30247}{2016^{2016}}\)
Vậy : A>B
Ta có
\(2016A=\frac{2016^{2017}+2016}{2016^{2017}+1}=\frac{2016^{2017}+1}{2016^{2017}+1}+\frac{2015}{2016^{2017}+1}=1+\frac{2015}{2016^{2017}+1}\)
\(2016B=\frac{2016^{2016}+2016}{2016^{2016}+1}=\frac{2016^{2016}+1}{2016^{2016}+1}+\frac{2015}{2016^{2016}+1}=1+\frac{2015}{2016^{2016}+1}\)
Do \(\frac{2015}{2016^{2017}+1}< \frac{2015}{2016^{2016}+1}\Rightarrow2016A< 2016B\Rightarrow A< B.\)
B = \(\frac{2016^{2015}+1}{2016^{2016}+1}\)< A =\(\frac{2016^{2016}+1}{2016^{2017}+1}\)
\(A=\frac{10^{2015}-1}{10^{2016}^{ }-1}=\frac{10^{2015}}{10^{2016}}=\frac{1}{1},B=\frac{10^{2014}-1}{10^{2015}-1}=\frac{10^{2014}}{10^{2015}}=\frac{1}{1}A=B\Rightarrow\)
( ghi lại đề )
Ta có :
\(15A=\frac{15^{2016}+15}{15^{2016}+1}=\frac{15^{2016}+1+14}{15^{2016}+1}=\frac{15^{2016}+1}{15^{2016}+1}+\frac{14}{15^{2016}+1}=1+\frac{14}{15^{2016}+1}\)
\(15B=\frac{15^{2015}+15}{15^{2015}+1}=\frac{15^{2015}+1+14}{15^{2015}+1}=\frac{15^{2015}+1}{15^{2015}+1}+\frac{14}{15^{2015}+1}=1+\frac{14}{15^{2015}+1}\)
Vì \(\frac{14}{15^{2016}+1}< \frac{14}{15^{2015}+1}\) nên \(1+\frac{14}{15^{2016}+1}< 1+\frac{14}{15^{2015}+1}\) hay \(15A< 15B\)
\(\Rightarrow\)\(A< B\)
Vậy \(A< B\)
Chúc bạn học tốt ~
nhan 2 ve voi 15