Question

S12 for the series 1+2+4+8+

Answer 1

$S_{12}=1+2+4+8+\cdots+2048$
$S_{12}=2^0+2^1+\cdots+2^{11}$
$2S_{12}=2^1+2^2+\cdots+2^{12}$

$\implies S_{12}-2S_{12}=2^0-2^{12}$
$-S_{12}=1-2^{12}$
$S_{12}=2^{12}-1$
$S_{12}=4096-1=4095$