Answer
$\sum ^{100}_{k=1}k\times 2^{k+2} $
Work Step by Step
$1\times 2^{3}+2\times 2^{1}+3\times 2^{5}+4\times 2^{6}+\dots +100\times 2^{102}=1\times 2^{1+2}+2\times 2^{2+2}+3\times 2^{3+2}+4\times 2^{4+2}+\dots+100\times 2^{100+2}=\sum ^{100}_{k=1}k\times 2^{k+2} $
