How can I express the series 2, 4, 6, 8, 10, 12 in summation notation?

The series 2, 4, 6, 8, 10, 12 consists of consecutive even numbers starting from 2. To express this series in summation notation, we first need to determine a general formula for the terms in the sequence.

The series can be viewed as the first six even numbers. We can express the
th even number using the formula 2n, where n is a positive integer.

Now, to represent the series 2, 4, 6, 8, 10, and 12 in summation notation, we can formulate it as follows:

Σ n=1⁶(2n)

In this notation:

• Σ denotes the summation symbol.
• n=1 indicates that we start summing from n=1.
• 6 is the upper limit, which tells us to sum up to the sixth term.
• 2n is the expression for each term in the series.

So, the final summation notation for the series 2, 4, 6, 8, 10, 12 is:

Σ n=1⁶(2n)

Using this notation allows for a concise and clear representation of the series, making it easier to analyze or further manipulate mathematically.