Question

What is the sum of the first n terms of this series?

4 + 6 + 8 + 10 + 12 + ⋯

Answer 1

its asking for the first n terms so your looking for a sum from 1 to n

Answer 2

...

Answer 3

The sigma notation isn't hard.

You are summing from \(i=1\) (from 4) till \(i=n\) (some nth term which we don't know, but don't need for the sigma)

Your pattern here is +2 every time, and you start from 4
Hint: (Think of a line that has a slope 2, and goes through the point (1,4) )

Answer 4

(I don't want to give it away, but do want to help.... apologize if it is not enough.

Answer 5

\(\sum_{k=1}^n(2k+2)=2\sum_{k=1}^nk+\sum_{k=1}^n2=2\dfrac{n(n+1)}{2}+2n=n^2+3n\)

Let me know if you have any questions.