Find the series:0,2,6,12,20and?

The series is represented by sum , . The remaining element of the series is 30.

Step-by-step explanation:

This exercise consist in deriving the function which contains every element of the given series. The sum that contains all elements of the series { 0, 2, 6, 12, 20,...} is represented by the following formula:

, (1)

Where is the cardinal associated with the element of the series.

Lastly, we proceed to evaluate the sum for the first five elements:

n = 0

n = 1

n = 2

n = 3

n = 4

The series is represented by sum , .

Lastly, the missing element is found by evaluating the function at , that is:

n = 5

The remaining element of the series is 30.