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BQ
1
2 tháng 7 2018
Đặt \(A=\frac{2^{2017}+1}{2^{2018}+1}\Rightarrow2A=\frac{2^{2018}+2}{2^{2018}+1}=\frac{2^{2018}+1+1}{2^{2018}+1}=1+\frac{1}{2^{2018}+1}\)
\(B=\frac{2^{2018}+1}{2^{2019}+1}\Rightarrow2B=\frac{2^{2019}+2}{2^{2019}+1}=\frac{2^{2019}+1+1}{2^{2019}+1}=1+\frac{1}{2^{2019}+1}\)
Vì \(2^{2019}+1>2^{2018}+1\Rightarrow\frac{1}{2^{2019}+1}< \frac{1}{2^{2018}+1}\)
\(\Rightarrow2A>2B\Rightarrow A>B\)
9 tháng 10 2018
\(C=\left(2018^{2019}+2018^{2018}+...+2018^2+2018\right)2017+1\)
\(=\left(2018^{2019}+2018^{2018}+...+2018^2+2018\right)2018-\left(2018^{2019}+2018^{2018}+...+2018\right)-1\)
\(=\left(2018^{2020}+2018^{2019}+...+2018^3+2018^2\right)-\left(2018^{2019}+2018^{2018}+...+2018^2+2018\right)+1\)\(=2018^{2020}-2018+1\)
\(=2018^{2020}-2017\)
BM
1
15 tháng 10 2018
\(M=\left(2018^{2019}+2018^{2018}+...+2018^2+2018\right)2017+1\)
Gọi \(A=2018^{2019}+2018^{2018}+...+2018^2+2018\)
\(\Rightarrow2018A=2018^{2020}+2018^{2019}+...+2018^3+2018^2\)
\(\Rightarrow2018A-A=2018^{2020}-2018\)
\(\Rightarrow2017A=2018^{2020}-2018\)
\(\Rightarrow A=\left(2018^{2020}-2018\right)\div2017\)
\(\Rightarrow M=\left(2018^{2020}-2018\right)\div2017.2017+1\)
\(\Rightarrow M=2018^{2020}-2018+1\)
\(\Rightarrow M=2018^{2020}-2017\)
TB
1
28 tháng 8 2019
A = 22019 - (22018 + 22017 +.....+ 21 + 20)
Đặt A1 = 22018 + 22017 +.....+ 21 + 20
⇒ 2A1 = 22019 + 22018 +.....+ 22 + 21
⇒ 2A1 - A1 = 22019 + 22018 +.....+ 22 + 21
- (22018 + 22017 +.....+ 21 + 20)
⇒ A1 = 22019 - 20
⇒ A = 22019 - A1
= 22019 -(22019 - 20)
= 22019 - 22019 + 1 = 1
vậy A = 1
PN
3
A=22019-(22018+22017+...+21+20)
Đặt M =22018+22017+...+21+20
M=22018+22017+...+2+1
2M=22019+22018+...+22+2
2M-M=(22019+22018+...+22+2)-(22018+22017+...+2+1)
M=22019-1
Suy ra:A=22019-(22019-1)
A=22019-22019+1
A=1
Vậy A=1
Ta có : \(A=2^{2019}-\left(2^{2018}+2^{2017}+...+2^1+2^0\right)\)
Đặt \(B=2^0+2^1+...+2^{2017}+2^{2018}\\ \Rightarrow2B=2+2^2+...+2^{2019}\\ \Rightarrow2B-B=\left(2+2^2+...+2^{2019}\right)-\left(2^0+2^1+...+2^{2017}+2^{2018}\right)\\ \Rightarrow B=2^{2019}-2^0\\ \Rightarrow A=2^{2019}-\left(2^{2019}-2^0\right)\\ \Rightarrow A=2^0=1\)
Vậy A=1