Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Vì \(2015^{2016}+1< 2015^{2017}+1\Rightarrow\frac{2015^{2016}+1}{2015^{2017}+1}< 1\)
\(\Rightarrow A=\frac{2015^{2016}+1}{2015^{2017}+1}< \frac{2015^{2016}+1+2014}{2015^{2017}+1+2014}=\frac{2015\left(2015^{2015}+1\right)}{2015\left(2015^{2016}+1\right)}=\frac{2015^{2015}+1}{2015^{2016}+1}=B\)
Vậy \(A< B\)
\(2015A=\frac{2015^{2017}+2015}{2015^{2017}+1}=\frac{2015^{2017}+1+2014}{2015^{2017}+1}=1+\frac{2014}{2015^{2017}+1}\)
\(2015B=\frac{2015^{2016}+2015}{2015^{2016}+1}=\frac{2015^{2016}+1+2014}{2015^{2016}+1}=1+\frac{2014}{2015^{2016}+1}\)
vì \(\frac{2014}{2015^{2017}+1}< \frac{2014}{2015^{2016}+1}\)
nên \(2015A< 2015B\)
=> \(B>A\)
A\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{2015}-\frac{1}{2016}\)
A=\(\frac{1}{1}+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{2015}-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{2016}\right)\)
A=\(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2015}+\frac{1}{2016}-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{2016}\right)\)
A=\(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2015}+\frac{1}{2016}-\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{1008}\right)\)
A=\(\frac{1}{1009}+\frac{1}{1010}+...+\frac{1}{2015}+\frac{1}{2016}\)
B-A=\(\left(\frac{1}{1008}+\frac{1}{1009}+\frac{1}{1010}+...+\frac{1}{2016}\right)-\left(\frac{1}{1009}+\frac{1}{1010}+...+\frac{1}{2015}+\frac{1}{2016}\right)\)
B-A=1/1008
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 = \(\frac{2015.2016-1}{2015.2016}\)= \(\frac{2015.2016}{2015.2016}\)\(-\)\(\frac{1}{2015.2016}\)= 1 \(-\)\(\frac{1}{2015.2016}\)
B = \(\frac{2016.2017-1}{2016.2017}\)= \(\frac{2016.2017}{2016.2017}\)\(-\)\(\frac{1}{2016.2017}\)= 1 \(-\)\(\frac{1}{2016.2017}\)
Vì \(\frac{1}{2015.2016}\)> \(\frac{1}{2016.2017}\)
=> 1 \(-\)\(\frac{1}{2015.2016}\)< \(1-\)\(\frac{1}{2016.2017}\)
=> A < B