Question

$\sum _{k=1}^4(2k+1)=$ .

Short answer

$\sum _{k=1}^4(2k+1)=\underline{24}$.

Step-by-step solution

Step 1. Given information 

The given expression is

$\sum _{k=1}^4(2k+1)$

Step 2. Value of expression

Evaluate the expression

$$\begin{gathered} \sum _{k=1}^4(2k+1)=\sum _{k=1}^{4}2k+\sum _{k=1}^{4}1 \\ =2\sum _{k=1}^{4}k+\sum _{k=1}^{4}1 \\ =2\left[\frac{4\left(4+1\right)}{2}\right]+1\left(4\right) \\ =4\left(5\right)+4 \\ =20+4 \\ =24 \end{gathered}$$

So the value of $\sum _{k=1}^4(2k+1)$is$24$.