Q. 16 - Calculus

Question

Fill in the blanks to complete each sum formula:

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

Step-by-Step Solution

Answer

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

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 $\sum _{k=1}^{n}1=\underline{n}.$