Answer
$3276$
Work Step by Step
We expand and simplify the sum:
$\displaystyle \sum_{j=1}^{6}3^{j+1}$
$=3^{1+1}+3^{2+1}+3^{3+1}+3^{4+1}+3^{5+1}+3^{6+1}$
$=3^{2}+3^{3}+3^{4}+3^{5}+3^{6}+3^{7}$
$=9+27+81+243+729+2187$
$=3276$
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