Question

Expand the partial sum and find its value:$\sum _{i=1}^{5}4i$

Short answer

The value of the partial sum is 60.

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thepartialsumisgivenas}\\ \sum _{i=1}^{5}4i\\ \text{Wehavetofindthevalueofthepartialsum.}\end{array}$

Step 2. Expand the partial sum

$\begin{array}{l}\text{Now,}\\ \text{Wesubstitutethevalues}1,2,3,4,5\text{inorder.}\\ \Rightarrow \sum _{i=1}^{5}4i=4\cdot 1+4\cdot 2+4\cdot 3+4\cdot 4+4\cdot 5\\ =4+8+12+16+20\\ =60\end{array}$