Question

Which of the following is the result of expanding the series

12
22
6x + 8
6x + 12

Answer 1

Answer: Third option.

Explanation:

Given
`3\\\sum(nx+2)\\n=0`, We know that indicates that we need to start with
`n=0` and finish with
`n=3`,

In order to expand the series, the procedure is the following:

`3\\\sum(nx+2)=(0x+2)+(1x+2)+(2x+2)+(3x+2)\\n=0\\\\3\\\sum(nx+2)=2+x+2+2x+2+3x+2\\n=0\\\\3\\\sum(nx+2)=6x+8\\n=0`

This result matches with the third option.

Answer 2

For this case we evaluate the series for each value of "n" from 0 to 3:

So:

`(0x + 2) + (1x + 2) + (2x + 2) + (3x + 2) =\\(0 + 2) + (x + 2) + (2x + 2) + (3x + 2) =\\2 + x + 2 + 2x + 2 + 3x + 2 =`

We add similar terms and we have the result of expanding the series is:

`8 + 6x`

ANswer:

Option C

`6x + 8`