so sánh: \(A=\dfrac{9^{2019}+1}{9^{2020}+1}\) và \(B=\dfrac{9^{2018}+1}{9^{2019}+1}\)
giúp mình với mn.
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Những câu hỏi liên quan
11 tháng 5 2023
\(A>\dfrac{2^{2018}}{2^{2018}+3^{2019}+5^{2020}}+\dfrac{3^{2019}}{2^{2018}+3^{2019}+5^{2020}}+\dfrac{5^{2020}}{5^{2020}+2^{2018}+3^{2019}}=1\)
\(B< \dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{2019\cdot2020}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2019}-\dfrac{1}{2020}\)
=>B<1
=>A>B
DX
1
AH
Akai Haruma
Giáo viên
14 tháng 5 2021
Lời giải:
Ta có:
\(A+1=\frac{2019^{2019}+2019^{2020}}{2019^{2019}-1}=\frac{2019^{2019}.2020}{2019^{2019}-1}\)
\(B+1=\frac{2019^{2019}+2019^{2018}}{2019^{2018}-1}=\frac{2019^{2018}.2020}{2019^{2018}-1}\) \(=\frac{2019^{2019}.2020}{2019^{2019}-2019}>\frac{2019^{2019}.2020}{2019^{2019}-1}\)
$\Rightarrow B+1>A+1$
$\Rightarrow B>A$
31 tháng 12 2022
a)= 2021.2021-2020.(2021+1)
= 2021.(2020+1)-2020.(2021+1)
= (2021.2020)+2021-(2020.2021)-2020
= 1
31 tháng 12 2022
b) B= (1+2-3-4)+(5+6-7-8)+(9+10-11-12)...........+(2017+2018-2019-2020)+2021
B= -4+(-4)+....................(-4)+2021
B= -4x505+2021
B= -2020 + 2021
B = 1
AH
Akai Haruma
Giáo viên
12 tháng 2 2023
Lời giải:
$A=1-\frac{1}{2019}+1-\frac{1}{2020}+1-\frac{1}{2021}+1+\frac{3}{2018}$
$=4+(\frac{1}{2018}-\frac{1}{2019}+\frac{1}{2018}-\frac{1}{2020}+\frac{1}{2018}-\frac{1}{2021})$
$> 4+0+0+0+0=4$
HT
1
KK
0
ND
Nguyễn Đức Trí
VIP
1 tháng 12 2023
\(A=\dfrac{2020^{2018}-1}{2020^{2019}+2019}\)
\(B=\dfrac{2020^{2019}+1}{2020^{2020}+2019}\)
Ta có :
\(A-B=\dfrac{2020^{2018}-1}{2020^{2019}+2019}-\dfrac{2020^{2019}+1}{2020^{2020}+2019}\)
\(\Rightarrow A-B=\dfrac{\left(2020^{2018}-1\right)\left(2020^{2020}+2019\right)-\left(2020^{2019}+2019\right)\left(2020^{2019}+1\right)}{\left(2020^{2019}+2019\right)\left(2020^{2020}+2019\right)}\)
\(\Rightarrow A-B=\dfrac{2020^{4038}+2019.2020^{2018}-2020^{2020}-2019-2020^{4038}-2020^{2019}-2019.2020^{2018}-2029}{\left(2020^{2019}+2019\right)\left(2020^{2020}+2019\right)}\)
\(\Rightarrow A-B=\dfrac{-\left(2020^{2020}+2020^{2019}+2.2019\right)}{\left(2020^{2019}+2019\right)\left(2020^{2020}+2019\right)}\)
mà \(\left\{{}\begin{matrix}-\left(2020^{2020}+2020^{2019}+2.2019\right)< 0\\\left(2020^{2019}+2019\right)\left(2020^{2020}+2019\right)>0\end{matrix}\right.\)
\(\Rightarrow A-B< 0\)
\(\Rightarrow A< B\)
Vậy ta được \(A< B\)
Lời giải:
\(9B=\frac{9^{2019}+9}{9^{2019}+1}=1+\frac{8}{9^{2019}+1}> 1+\frac{8}{9^{2020}+1}=\frac{9^{2020}+9}{9^{2020}+1}=9A\)
$\Rightarrow B>A$