\(B=1+5+5^2+5^3+...+5^{2008}+5^{2009}\)
\(\Rightarrow5B=5\left(1+5+5^2+5^3+...+5^{2008}+2^{2009}\right)\)
\(5B=5+5^2+5^3+5^4+...+2^{2009}+2^{2010}\)\(\Rightarrow4B=5B-B=\left(5+5^2+5^3+5^4+...+5^{2009}+5^{2010}\right)-\left(1+5+5^2+5^3+...+5^{2008}+5^{2009}\right)\)
\(4B=5^{2010}-1\Leftrightarrow B=\dfrac{5^{2010}-1}{4}\) vậy \(B=\dfrac{5^{2010}-1}{4}\)