Question

Sigma Notation Write the sum without using sigma notation.

$\sum _{k=0}^6\sqrt{k+4}$

Short answer

The sum is$\sqrt{5}+\sqrt{6}+\sqrt{7}+\sqrt{8}+\sqrt{9}+\sqrt{10}.$

Step-by-step solution

Step 1.  Given

The given sequence is$\sum _{k=0}^6\sqrt{k+4}.$

Step 2.  To determine

We have to write the sum without using sigma notation.

Step 3.  Calculation

We’ll plug the values for k, to get rid of the sigma notation.

$\begin{array}{l}\sum _{k=0}^6\sqrt{k+4}\\ =\sqrt{1+4}+\sqrt{2+4}+\sqrt{3+4}+\sqrt{4+4}+\sqrt{5+4}+\sqrt{6+4}\\ =\sqrt{5}+\sqrt{6}+\sqrt{7}+\sqrt{8}+\sqrt{9}+\sqrt{10}\end{array}$

Hence the sum is$\sqrt{5}+\sqrt{6}+\sqrt{7}+\sqrt{8}+\sqrt{9}+\sqrt{10}$.