Question

Expand the partial sum and find its value:$\sum _{i=1}^{5}3i$

Short answer

The value of the partial sum is 45.

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thepartialsumisgivenas}\\ \sum _{i=1}^{5}3i\\ \text{Wehavetofindthevalueofthepartialsum.}\end{array}$

Step 2. Expand the partial sum

$\begin{array}{l}\text{Now,}\\ \text{Wesubstitutethevalues}1,2,3,4,5\text{inorder.}\\ \Rightarrow \sum _{i=1}^{5}3i=3\cdot 1+3\cdot 2+3\cdot 3+3\cdot 4+3\cdot 5\\ =3+6+9+12+15\\ =45\end{array}$