Question

In the following exercises, write each sum using summation notation.

$4+2+\frac{4}{3}+1+\frac{4}{5}$

Short answer

The summation notation is$\sum _{n=1}^5\frac{4}{n}$.

Step-by-step solution

Step 1. Given information.

The given expression is,

$4+2+\frac{4}{3}+1+\frac{4}{5}$.

Step 2. Finding summation notation.

Here, the numerators are all $4$'s and the denominators are numbers from $1$to $5$then we get,

$$\begin{gathered} 4+2+\frac{4}{3}+1+\frac{4}{5} \\ n:1,2,3,4,5 \\ Terms:4,2,\frac{4}{3},1,\frac{4}{5} \\ Pattern:\frac{4}{1},\frac{4}{2},\frac{4}{3},\frac{4}{4},\frac{4}{5}......\frac{4}{n} \end{gathered}$$

Then the sum can be written in the form of summation notation that is

$4+2+\frac{4}{3}+1+\frac{4}{5}=\sum _{n=1}^5\frac{4}{n}$.