Answer
$700$
Work Step by Step
$\sum ^{4}_{k=1}\left( k+1\right) ^{k}=\left( 1+1\right) ^{1}+\left( 2+1\right) ^{2}+\left( 3+1\right) ^{3}+\left( 4+1\right) ^{4}=2+9+64+625=700$
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