Giá trị của \(\begin{aligned} & \mathrm{B}=3+3^{3}+3^{5}+3^{7}+\ldots+3^{29} \end{aligned}\) là

* Hướng dẫn giải

 \(\begin{aligned} &\text {Ta có } \mathrm{B}=3+3^{3}+3^{5}+3^{7}+\ldots+3^{29} \\ &=\left(3+3^{3}+3^{5}\right)+\left(3^{7}+3^{9}+3^{11}\right)+\ldots+\left(3^{25}+3^{27}+3^{29}\right) \\ &=273+3^{6}\left(3+3^{3}+3^{5}\right)+\ldots+3^{24}\left(3+3^{3}+3^{5}\right) \\ &=273+3^{6} \cdot 273+\ldots+3^{24} \cdot 273=273 \cdot\left(1+3^{6}+\ldots+3^{24}\right) \end{aligned}\)