Chris Y. answered • 05/14/19
State-certified high school Calculus teacher with 3+ years experience
The trick is to write what you know and then break it apart to look similar to the form that they're asking for.
What we know:
This is an arithmetic series, increasing by the same value (3) each time, so I know the summation formula will look like a*n + b (different from the "A" and "B" in the original problem). The "a" here is going to be the value the series increases by, so 3. The "b" you have to find.
So I know my summation formula is 3n + b. I also know that when n = 1 this should give me 6. Then:
3n + b = 6, and so b = 3.
The formula for this series is then 3n + 3, and the series is then ∑(3n + 3).
BUT, they want this to look like A∑B, meaning they want some factor in front of the summation sign. Looking at the summation formula we found, ∑(3n + 3), is there anything we can factor out to the front? There is a 3 in common among all terms, so we can write this as
3∑(n+1)
and compare to
A∑B
Now I can just match between the two and say that A = 3 and B = n+1
