\(B=3^1+3^2+3^3+...+3^{2010}\)
\(\Rightarrow3B=3^2+3^3+3^4+...+3^{2011}\)
\(\Rightarrow3B-B=2B=\left(3^2+3^3+3^4+...+3^{2011}\right)-\left(3+3^2+3^3+...+3^{2010}\right)\)
\(\Rightarrow2B=3^{2011}-3\)
\(\Rightarrow B=\frac{3^{2011}-3}{2}\)
Vậy \(B=\frac{3^{2011}-3}{2}\)
_Chúc bạn học tốt_
\(B=3^1+3^2+3^3+...+3^{2010}\)
\(3B=3^2+3^3+3^4+...+3^{2011}\)
\(3B-B=\left(3^2+3^3+3^4+...+3^{2011}\right)-\left(3^1+3^2+3^3+...+3^{2010}\right)\)
\(2B=3^{2011}-3\)
\(B=\frac{3^{2011}-3}{2}\)
Vậy \(B=\frac{3^{2011}-3}{2}\)
Chúc bạn học tốt ~