Mathematics - Sequence & Series Question with Solution | TestHub

$S^{\text{'}}=2^{10}+2^9·3+2^8·3^2+\dots \dots .+2·3^9+3^{10}$

$S^{\text{'}}=2^{10}\left\{1+\frac{3}{2}+{\left(\frac{3}{2}\right)}^2+\dots \dots .+{\left(\frac{3}{2}\right)}^9+{\left(\frac{3}{2}\right)}^{10}\right\}$

G.P. $\to \mathrm{a}=1,r=\frac{3}{2},n=11$

$S^{\text{'}}=2^{10}·\left\{\frac{{\left(\frac{3}{2}\right)}^{11}-1}{\frac{3}{2}-1}\right\}=2^{11}\left(\frac{3^{11}}{2^{11}}-1\right)$

$=3^{11}-2^{11}$