Ta có: \(A=1+3^2+3^4+3^6+...+3^{2008}\)
\(\Leftrightarrow3A=3^1+3^3+3^5+...+3^{2009}\)
\(\Leftrightarrow A+3A=1+3^1+3^2+3^3+...+3^{2009}\)
\(\Leftrightarrow4A=1+3^1+3^2+...+3^{2009}\)
\(\Leftrightarrow12A=3^1+3^2+3^3+...+3^{2010}\)
\(\Leftrightarrow12A-4A=3^{2010}-1\)
\(\Leftrightarrow8A=3^{2010}-1\)
Lại có: B=8A-32010
\(\Leftrightarrow B=3^{2010}-1-3^{2010}=0-1=\left(-1\right)\)
Vậy B=(-1)
A = 1+32+34+..........+32008
=> A = 30+32+34+.......+32008
=> 9A = 32+34+36+.........+32010
=> 9A -A= 32+34+36+.........+32010- 30+32+34+.......+32008
=> 8A = 32010- 1
=> 8A -32010= 32010- 1 -32010
=> 8A -32010 = -1
=> B = -1
