Question

Express the series in summation notation.

2 + 4 + 6 + 8 + 10 + 12

Answer 1

`\sum _(n = 1) ^(6) 2n`

Step-by-step explanation

The series is:

2 + 4 + 6 + 8 + 10 + 12

The first term is:

f(1)=2

The common difference is

`d= 4 - 2 = 2`

The formula for the corresponding sequence is

`f(n) = 2 + 2(n - 1)`

`f(n) = 2 + 2n - 2`

`f(n) = 2n`

The summation notation is:

`\sum _(n = 1) ^(6) 2n`