Question

Fill in the blanks to complete each sum formula:

$\sum _{k=1}^{n}1=\underline{}$

Short answer

The complete sum formula is$\sum _{k=1}^{n}1=\underline{n}.$

Step-by-step solution

Step 1. Given information.

Given incomplete sum formula is following.

$\sum _{k=1}^{n}1=\underline{}$

Step 2. Explanation.

Expand the sigma notation

$$\begin{gathered} \sum _{k=1}^{n}1=1+1+\cdots +1\dots (n^{th}\mathrm{times})=n \\ \sum _{k=1}^{n}1=n. \end{gathered}$$

So complete sum formula is$\sum _{k=1}^{n}1=\underline{n}.$