Tính tổng B = 2 + 2^3 + 2^5 + 2^7 + + 2^2009

B = 2 + \({2^3} + {2^5} + {2^7} + ... + {2^{2009}}\)

\[\begin{array}{l} \Leftrightarrow {2^2}.B = {2^3} + {2^5} + {2^9} + {...2^{2011}}\\ \Leftrightarrow 4B = {2^3} + {2^5} + {2^9} + {...2^{2011}}\\ \Leftrightarrow 4B - B = {2^{2011}} - 2\end{array}\]

\( \Leftrightarrow 3B = {2^{2011}} - 2 \Leftrightarrow B = \frac{{{2^{2011}} - 2}}{3}\).