Answer
$n(n+1)$
Work Step by Step
We simplify:
$\displaystyle \sum_{i=1}^{n}2i$
We can take out $2$ because it is a constant $(\sum{cx}=c\sum{x})$:
$=2\sum_{i=1}^{n}i$
We know that $\sum_{i=1}^{n}i=\frac{n(n+1)}{2}$, so:
$=2*\frac{n(n+1)}{2}$
$=n(n+1)$