So sánh: 1998/1999+1999/2000 va 1998+1999/1999+2000
So sánh: 1998/1999+1999/2000 va 1998+1999/1999+2000
Đặt A=1998/1999+1999/2000 B=1998+1999/1999+2000 =1998/1999+2000 + 1999/1999+2000 Vì 1998/1998>1998/1999+2000 1999/2000>1999/1999+2000 Nên A>B
So sánh:
\(A=\dfrac{1999^{1999}+1}{1999^{1998}+1}\) ; \(B=\dfrac{1999^{2000}+1}{1999^{1999}+1}\)
Giúp với!
So sánh
\(A=\dfrac{1999^{1999}+1}{1999^{1998}+1}\) ; \(B=\dfrac{1999^{2000}+1}{1999^{1999}+1}\)
Ta có: \(B=\dfrac{1999^{2000}+1}{1999^{1999}+1}>1\) ( vì tử > mẫu )
Do đó: \(B=\dfrac{1999^{2000}+1}{1999^{1999}+1}>\dfrac{1999^{2000}+1+1998}{1999^{1999}+1+1998}=\dfrac{1999^{2000}+1999}{1999^{1999}+1999}=\dfrac{1999.\left(1999^{1999}+1\right)}{1999.\left(1999^{1998}+1\right)}=\dfrac{1999^{1999}+1}{1999^{1998}+1}=A\)
Vậy B > A
Chúc bạn học tốt
So sánh: C=\frac{1999^2000+1/1999^1999+1} và D=\frac{1999^1999+1/1999^1998+1}
So sánh: C=1999^2000+1/1999^1999+1và D=1999^1999+1/1999^1998+1
Giúp với mình đang cần gấp
SO sánh A và B Biết A=1999^1999+1/1999^2000 +1va B=1999^1998+1/1999^1999+1
3k cho câu trả lời đúng
ta thấy 19991999 + 1 / 19992000 + 1 < 1 và 1998 > 0
nên ta có: A < 19991999 + 1 + 1998 / 19992000 + 1 + 1998
< 19991999 + 1999 / 19992000 + 1999
< 1999(19991998 + 1) / 1999(19991999 + 1)
< 19991998 + 1 / 19991999 + 1
< B
Vậy A < B
để tui xem lại đã hink như tui làm bài này zùi
So sánh 2 số A= 1998*2000 va B= 1999^2
A=1998.2000=1998.(1999+1)=1998.1999+1998
1999.1999=1998.1999+1999
=>A<B
vậy A<B
So sánh 1999×2000-2/1998×1999+3997 với 1
1999x2000-2/1998x1999+3997
=1999x(1998+2)-2/1998x1999+3997
=1999x1998+3998-2/1998x1999+3997
=1999x1998+3996/1998x1999+3997
=3996/3997
=> 3996/3997 < 1
Vậy 1999x2000-2/1998x1999+3997 < 1
So sánh; A =19991999 + 1/ 19991998 + 1 và B = 19992000 + 1/ 19991999 +1
ta có: \(A=\frac{1999^{1999}+1}{1999^{1998}+1}=\frac{1999.\left(1999^{1998}+1\right)-1998}{1999^{1998}+1}=\frac{1999.\left(1999^{1998}+1\right)}{1999^{1998}+1}-\frac{1998}{1999^{1998}+1}\)
\(=1999-\frac{1998}{1999^{1998}+1}\)
\(B=\frac{1999^{2000}+1}{1999^{1999}+1}=\frac{1999.\left(1999^{1999}+1\right)-1998}{1999^{1999}+1}=\frac{1999.\left(1999^{1999}+1\right)}{1999^{1999}+1}-\frac{1998}{1999^{1999}+1}\)
\(=1999-\frac{1998}{1999^{1999}+1}\)
mà \(\frac{1998}{1999^{1998}+1}>\frac{1998}{1999^{1999}+1}\Rightarrow1999-\frac{1998}{1999^{1998}+1}< 1999-\frac{1998}{1999^{1999}+1}\)
\(\Rightarrow A< B\)
so sánh:A=1999^1999+1/1999^1998+1
B=1999^2000+1/1999^1999+1
\(A=\dfrac{1999^{1999}+1}{1999^{1998}+1}\)
\(\dfrac{1}{1999}A=\dfrac{1999^{1999}+1}{1999^{1999}+1999}\)
\(\dfrac{1}{1999}A=\dfrac{1999^{1999}}{1999^{1999}}-\dfrac{1998}{1999^{1999}+1999}\)
\(\dfrac{1}{1999}A=1-\dfrac{1998}{1999^{1999}+1999}\)
\(B=\dfrac{1999^{2000}+1}{1999^{1999}+1}\)
\(\dfrac{1}{1999}B=\dfrac{1999^{2000}+1}{1999^{2000}+1999}\)
\(\dfrac{1}{1999}B=\dfrac{1999^{2000}}{1999^{2000}}-\dfrac{1998}{1999^{2000}+1999}\)
\(\dfrac{1}{1999}B=1-\dfrac{1998}{1999^{2000}+1999}\)
Vì \(\dfrac{1998}{1999^{1999}+1999}>\dfrac{1998}{1999^{2000}+1999}=>\dfrac{1}{1999}A< \dfrac{1}{1999}B=>A< B\)
\(A=\dfrac{1999^{1999}+1}{1999^{1998}+1}=\dfrac{\left(1999^{1999}+1\right)^2}{\left(1999^{1998}+1\right)\left(1999^{1999}+1\right)}\)
\(A=\dfrac{\left(1999^{1999}\right)^2+2.1999^{1999}+1}{\left(1999^{1998}+1\right)\left(1999^{1999}+1\right)}\left(1\right)\)
\(B=\dfrac{1999^{2000}+1}{1999^{1999}+1}=\dfrac{\left(1999^{2000}+1\right)\left(1999^{1998}+1\right)}{\left(1999^{1998}+1\right)\left(1999^{1999}+1\right)}\)
\(B=\dfrac{\left(1999.1999^{1999}+1\right)\left(\dfrac{1}{1999}.1999^{1999}+1\right)}{\left(1999^{1998}+1\right)\left(1999^{1999}+1\right)}\)
\(B=\dfrac{\left(1999^{1999}\right)^2+1999.1999^{1999}+\dfrac{1}{1999}.1999^{1999}+1}{\left(1999^{1998}+1\right)\left(1999^{1999}+1\right)}\)
\(B=\dfrac{\left(1999^{1999}\right)^2+\left(1999+\dfrac{1}{1999}\right).1999^{1999}+1}{\left(1999^{1998}+1\right)\left(1999^{1999}+1\right)}\left(2\right)\)
mà \(\left(1999+\dfrac{1}{1999}\right)>2\)
\(\left(1\right).\left(2\right)\Rightarrow A< B\)
Sửa dòng cuối chỗ ''Vì phần mẫu của \(A< B\)'' thành ''Vì phần mẫu của \(\dfrac{1998}{1999^{1999}+1999}< \dfrac{1998}{1999^{2000}+1999}\)'' nhé.