K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Các câu hỏi dưới đây có thể giống với câu hỏi trên
LM
2
KT
15 tháng 8 2018
\(A=\frac{2017\times2108}{2017\times2018+1}=1-\frac{1}{2017\times2018+1}\)
\(B=\frac{2018\times2019}{2018\times2019+1}=1-\frac{1}{2018\times2019+1}\)
Nhận thấy:\(2017\times2018< 2018\times2019\)
=> \(2017\times2018+1< 2018\times2019+1\)
=> \(\frac{1}{2017\times2018+1}>\frac{1}{2018\times2019+1}\)
=> \(A< B\)
DL
11 tháng 6 2018
Bài 1:
Ta có:
\(N=\frac{2017+2018}{2018+2019}=\frac{2017}{2018+2019}+\frac{2018}{2018+2019}\)
Do \(\hept{\begin{cases}\frac{2017}{2018+2019}< \frac{2017}{2018}\\\frac{2018}{2018+2019}< \frac{2018}{2019}\end{cases}\Rightarrow\frac{2017}{2018+2019}+\frac{2018}{2018+2019}< \frac{2017}{2018}+\frac{2018}{2019}}\)
\(\Leftrightarrow N< M\)
Vậy \(M>N.\)
Bài 2:
Ta có:
\(A=\frac{2017}{987653421}+\frac{2018}{24681357}=\frac{2017}{987654321}+\frac{2017}{24681357}+\frac{1}{24681357}\)
\(B=\frac{2018}{987654321}+\frac{2017}{24681357}=\frac{1}{987654321}+\frac{2017}{987654321}+\frac{2017}{24681357}\)
Do \(\hept{\begin{cases}\frac{2017}{987654321}+\frac{2017}{24681357}=\frac{2017}{987654321}+\frac{2017}{24681357}\\\frac{1}{24681357}>\frac{1}{987654321}\end{cases}}\)
\(\Rightarrow\frac{2017}{987654321}+\frac{2017}{24681357}+\frac{1}{24681357}>\frac{1}{987654321}+\frac{2017}{987654321}+\frac{2017}{24681357}\)
\(\Leftrightarrow A>B\)
Vậy \(A>B.\)
Bài 3:
\(\frac{2016}{2017}+\frac{2017}{2018}+\frac{2018}{2019}+\frac{2019}{2016}=1-\frac{1}{2017}+1-\frac{1}{2018}+1-\frac{1}{2019}+1+\frac{3}{2016}\)
\(=1+1+1+1-\frac{1}{2017}-\frac{1}{2018}-\frac{1}{2019}+\frac{3}{2016}\)
\(=4-\left(\frac{1}{2017}+\frac{1}{2018}+\frac{1}{2019}-\frac{3}{2016}\right)\)
Do \(\hept{\begin{cases}\frac{1}{2017}< \frac{1}{2016}\\\frac{1}{2018}< \frac{1}{2016}\\\frac{1}{2019}< \frac{1}{2016}\end{cases}\Rightarrow\frac{1}{2017}+\frac{1}{2018}+\frac{1}{2019}< \frac{1}{2016}+\frac{1}{2016}+\frac{1}{2016}=\frac{3}{2016}}\)
\(\Rightarrow\frac{1}{2017}+\frac{1}{2018}+\frac{1}{2019}-\frac{3}{2016}\)âm
\(\Rightarrow4-\left(\frac{1}{2017}+\frac{1}{2018}+\frac{1}{2019}-\frac{3}{2016}\right)>4\)
Vậy \(\frac{2016}{2017}+\frac{2017}{2018}+\frac{2018}{2019}+\frac{2019}{2016}>4.\)
Bài 4:
\(\frac{1991.1999}{1995.1995}=\frac{1991.\left(1995+4\right)}{\left(1991+4\right).1995}=\frac{1991.1995+1991.4}{1991.1995+4.1995}\)
Do \(\hept{\begin{cases}1991.1995=1991.1995\\1991.4< 1995.4\end{cases}}\Rightarrow1991.1995+1991.4< 1991.1995+1995.4\)
\(\Rightarrow\frac{1991.1995+1991.4}{1991.1995+4.1995}< \frac{1991.1995+1995.4}{1991.1995+4.1995}=1\)
\(\Rightarrow\frac{1991.1999}{1995.1995}< 1\)
Vậy \(\frac{1991.1999}{1995.1995}< 1.\)
DH
1
22 tháng 7 2015
15/27 < 31/54
1965/1967 > 1973/1975 tick đúng nha Dao Huong Giang
10 tháng 6 2018
mình ko ghi lại đề nha
a) \(1-\frac{2004}{2005}=\frac{1}{2005}\);\(1-\frac{2005}{2006}=\frac{1}{2006}\)
ta thấy \(\frac{1}{2005}>\frac{1}{2006}\)
=> \(\frac{2004}{2005}< \frac{2005}{2006}\)
b)\(\frac{2007}{2006}-1=\frac{1}{2006};\frac{2006}{2005}-1=\frac{1}{2005}\)
ta thấy \(\frac{1}{2006}< \frac{1}{2005}\)
=>\(\frac{2007}{2006}< \frac{2006}{2005}\)
c) ta có \(\frac{1975}{2005}>\frac{1975}{2006}>\frac{1974}{2006}\)
=>\(\frac{1975}{2005}>\frac{1974}{2006}\)
1975 . 2018 - 1
= 3985550 - 1
= 3985549
1974 + 1975 . 2017
= 1974 + 3983575
= 3985549
lưu ý: dấu chấm là dấu nhân
cố luyện khả năng tính toán nha bạn!!!