Be De no bi dien rui ak

VAY NO BI DIEN

Bọn mày ko giúp thì cút

1000^999>999^1000

\(A=\frac{1000^{2004}+1}{1000^{2005}+1}\)

=> \(1000A=\frac{1000^{2005}+1000}{1000^{2005}+1}=1+\frac{999}{1000^{2005}+1}\)

\(B=\frac{1000^{2005}+1}{1000^{2006}+1}\)

=> \(1000A=\frac{1000^{2006}+1000}{1000^{2006}+1}=1+\frac{999}{1000^{2006}+1}\)

Vì: \(1000^{2006}+1>1000^{2005}+1\)

=> \(\frac{999}{1000^{2006}+1}< \frac{99}{1000^{2005}+1}\)

=> \(1+\frac{999}{1000^{2006}+1}< 1+\frac{99}{1000^{2005}+1}\)

=>  1000B < 1000A 

=> B < A

tất nhiên 1000x1000 lớn hơn rồi

999x1001=999x(1000+1)=999x1000+999x1

1000x1000=(999+1)x1000=999x1000+1000x1

vì 999x1>1000x1 nên : 999x1000+999x1>999x1000+1000x1

hay 999x1001>1000x1000

so sánh A=\(\frac{1000+1010}{2015+2016}\) và B=\(\frac{1000}{2015}+\frac{1010}{2016}\)

ta có:\(\frac{1000+1010}{2015+2016}=\frac{1000}{2015+2016}+\frac{1010}{2015+2016}\)

mà \(\frac{1000}{2015+2016}<\frac{1000}{2015}\) và \(\frac{1010}{2015+2016}<\frac{1010}{2016}\)

=>A=1000+1010/2015+2016 <B=1000/2015+1010/2016

DÙng máy tính rồi tính tui ko rảnh mà giải cho đâu

\(\frac{2015}{2016}< \frac{2016}{2017}\)

\(\frac{1000}{100}< \frac{1000}{99}\)

nhé bạn

2015/2016<2016/2017

1001/1000<1000/999

Đặt a=1000^2012 thì \(A=\frac{a+2}{a-1}\)   ;   \(B=\frac{a}{a-3}\)

Xét    \(A-B=\frac{a+2}{a-1}-\frac{a}{a-3}=\frac{\left(a+2\right)\left(a-3\right)-a\left(a-1\right)}{\left(a-1\right)\left(a-3\right)}\)

                      \(=\frac{a^2-a-6-a^2+a}{\left(a-1\right)\left(a-3\right)}=\frac{-6}{\left(a-1\right)\left(a-3\right)}\)

Do \(a>1;a>3\)  nên \(\left(a-1\right)\left(a-3\right)>0\Leftrightarrow A-B< 0\)

 Do đó \(A>B\)