Answer
$\sum\limits_{k=2}^{6}{\sqrt{5k-1}}$ is $21.3847.$
Work Step by Step
$\sum\limits_{k=2}^{6}{\sqrt{5k-1}}$
Here, the value of $k$ starts at $2$ and ends with $6$:
For the sum of the notation,
$\begin{align}
& \sum\limits_{k=2}^{6}{\sqrt{5k-1}}=\sqrt{5\cdot 2-1}+\sqrt{5\cdot 3-1}+\sqrt{5\cdot 4-1}+\sqrt{5\cdot 5-1}+\sqrt{5\cdot 6-1} \\
& =\sqrt{9}+\sqrt{14}+\sqrt{19}+\sqrt{24}+\sqrt{29} \\
& \approx 21.3847
\end{align}$
Thus, the sum of the sigma notation $\sum\limits_{k=2}^{6}{\sqrt{5k-1}}$ is $21.3847$.
