Express the series in summation notation: 2, 4, 6, 8, 10, 12

The given series is: 2, 4, 6, 8, 10, 12. This is an arithmetic series where each term increases by 2.

To express this series in summation notation, we first identify a general term for the series. We can observe that the nth term can be expressed as:

a_n = 2n

for n = 1, 2, 3, 4, 5, 6. Here, when n = 1, a_n = 2(1) = 2; when n = 2, a_n = 2(2) = 4, and so forth.

Now, we can write the series in summation notation as:

∑_n=1⁶ 2n

This indicates that we are summing the terms of the series starting from n = 1 to n = 6.