Answer
$\sum\limits_{k=1}^{6}{\sqrt{k}}$.
Work Step by Step
$1+\sqrt{2}+\sqrt{3}+2+\sqrt{5}+\sqrt{6}$
This is the sum of the root of the first six natural numbers.
The value of $k$ varies from $1$ to $6$.
Thus, the sigma notation is,
$\sum\limits_{k=1}^{6}{\sqrt{k}}$
Thus, the sigma notation for the sum $1+\sqrt{2}+\sqrt{3}+2+\sqrt{5}+\sqrt{6}$ is $\sum\limits_{k=1}^{6}{\sqrt{k}}$.
