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a) \(A=3^1+3^2+3^3+...+3^{2010}\)
\(3A=3.\left(3^1+3^2+3^3+...+3^{2010}\right)\)
\(3A=3.3^1+3.3^2+3.3^3+...+3.3^{2010}\)
\(3A=3^2+3^3+3^4+...+3^{2011}\)
\(3A-A=2A\)
\(2A=\left(3^2+3^3+3^4+...+3^{2011}\right)-\left(3^1+3^2+3^3+...+3^{2010}\right)\)
\(2A=3^{2011}-3^1=3^{2011}-3\)\(\Rightarrow\)\(A=\left(3^{2011}-3\right)\div2\)
b) Mình ko biết
-Ta có:1+2+3+.........+2006=(2006+1).2006:2=2013021
A=31+
\(A=3^1+3^2+3^3+...+3^{2010}\)
\(\Rightarrow3A=3^2+3^3+...+3^{2011}\)
\(\Rightarrow2A=3^{2011}-3\)
\(\Rightarrow A=\frac{3^{2011}-2}{2}\)
\(\Leftrightarrow2A+3=3^{2011}-3+3=2^{2011}\)
\(\Rightarrow x=2011\)
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
3A = 32 + 33 + 34 + ... +32007
=> 3A - A = 2A = 32007 - 31 = 3( 32006-1)
=>A = \(\frac{3\left(3^{2006}-1\right)}{2}\)
Ta có : 2A + 3 = 32007 + 3 - 3
= 32007 = 3x
=> x= 2007
b)
A = \(\frac{1.5.6+2^3.1.5.6+4^3.1.5.6+9^3.1.5.6}{1.3.5+2^3.1.3.5+4^3.1.3.5+9^3.1.3.5}\)= \(\frac{1.5.6\left(1+2^3+4^3+9^3\right)}{1.3.5\left(1+2^3+4^3+9^3\right)}\)=2
\(A=3+3^2+3^3+...+3^{2006}\)
\(\Leftrightarrow3A=3\left(3+3^2+3^3+....+3^{2006}\right)\)
\(\Leftrightarrow3A=3^2+3^3+3^4+....+3^{2007}\)
\(\Leftrightarrow3A-A=\left(3^2+3^3+3^4+...+3^{2007}\right)-\left(3+3^2+3^3+...+3^{2006}\right)\)
\(\Leftrightarrow2A=3^{2007}-3\)
\(\Leftrightarrow A=\frac{3^{2007}-3}{2}\)
Ta có \(2A=3^{2007}-3\)
=> 2A+3=\(3^{2007}-3+3=3^{2007}\)
=> x=2007
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:\(2A=3^{2011}-3\Rightarrow2A+3=3^{2011}\Rightarrow x=2011\)