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trả lời câu c nha
A=3+3^2 +3^+...+3^99+3^100
3A=3^2+3^3+...+3^100+3^101
3A-A=2A=3^101-3
Do đó 2A+3=3^101.Theo đề bài,2A+3=3^x
Vậy x=101
^ là mụ nha
3A=3^2+3^3+...+3^2007
=>3a-A=(3^2+3^3+...+3^2007)-(3^1+3^2+...+3^2006)
=>2A=3^2007-3^1=3^2007-3
=>2A+3=3^2007-3+3=3^2007=3^x
=>x=2007
B=3+3^2+...+3^100.
3B=3.3+3^2.3+...+3^100.3
3B=3^2+3^3+...+3^101
3B-B=(3^2+3^3+...+3^101)-(3+3^2+...+3^100)
2B=3^101-3
Mà2B+3=3^n
Suy ra:3^101-3+3=3^n
3^n+3^101
Vậy n=101
Bài 1(b) làm tương tự,còn bài (a) thì bạn tự làm
a,Ta có:3A=32+33+................+32011
\(\Rightarrow3A-A=\left(3^2+3^3+.....+3^{2011}\right)-\left(3+3^2+.....+3^{2010}\right)\)
\(\Rightarrow2A=3^{2011}-3\)
\(\Rightarrow A=\frac{3^{2011}-3}{2}\)
b,Ta có:\(2A=3^{2011}-3\Rightarrow2A+3=3^{2011}\Rightarrow x=2011\)
3A - A = (32 + 33 + 34 + ... + 32007) - (3 + 32 + 33 + ... + 32006)
2A = 32007 - 3\(\Rightarrow\hept{\begin{cases}A=\frac{3^{2007}-3}{2}\\2A+3=3^{2007}\Rightarrow x=2007\end{cases}}\)
\(A=3+3^2+3^3+...+3^{2016}\)
\(\Rightarrow3A=3\left(3+3^2+3^3+...+3^{2016}\right)\)
\(\Rightarrow3A=3^2+3^3+3^4+...+3^{2017}\)
\(\Rightarrow3A-A=\left(3^2+3^3+3^4+...+3^{2017}\right)-\left(3+3^2+3^3+3^{2016}\right)\)
\(\Rightarrow2A=-3+3^{2017}\)
\(\Rightarrow A=\frac{3+3^{2017}}{2}\)
b) \(2A+3=-3+3-3^{2017}=3^{2017}=3^x\)
\(\Rightarrow x=2017\)
\(A=3+3^2+3^3+...+3^{2006}\)
\(\Leftrightarrow3A=3\left(3+3^2+3^3+....+3^{2006}\right)\)
\(\Leftrightarrow3A=3^2+3^3+3^4+....+3^{2007}\)
\(\Leftrightarrow3A-A=\left(3^2+3^3+3^4+...+3^{2007}\right)-\left(3+3^2+3^3+...+3^{2006}\right)\)
\(\Leftrightarrow2A=3^{2007}-3\)
\(\Leftrightarrow A=\frac{3^{2007}-3}{2}\)
Ta có \(2A=3^{2007}-3\)
=> 2A+3=\(3^{2007}-3+3=3^{2007}\)
=> x=2007
Ta có : \(A=3+3^2+3^3+......+3^{2006}\)
=> \(3A=3^2+3^3+......+3^{2007}\)
=> \(3A-A=3^{2007}-3\)
=> \(2A=3^{2007}-3\)
=> \(A=\frac{3^{2007}-3}{2}\)
b) Ta có : \(2A=3^{2007}-3\) (theo ý a)
=> \(2A+3=3^{2007}\)
=> x = 2007
\(A=3+3^2+3^3+.........+3^{2006}\)
\(\Leftrightarrow3A=3^2+3^3+.........+3^{2007}\)
\(\Leftrightarrow3A-A=\left(3^2+3^3+.......+3^{2007}\right)-\left(3+3^2+.....+3^{2006}\right)\)
\(\Leftrightarrow2A=3^{2007}-3\)
\(\Leftrightarrow A=\frac{3^{2007}-3}{2}\)
\(\Leftrightarrow2A+3=3^{2007}\)
\(\Leftrightarrow3^x=3^{2007}\)
\(\Leftrightarrow x=2007\left(tm\right)\)
A=3+32+33+...+32019
3A=32+33+...+32020
3A-A=(32+33+...+32020)-(3+32+33+...+32019)
2A=32020-3
2A+3=32020
⇒n=2020