Question

Back already my brain is freid and i cant figure this one out im having trouble converting it into a definite integral
https://i.gyazo.com/09e50d99173dd0bc2ee0c7c08bcd7de8.png

Answer 1

where is 2/n? i can move the 3 out but then how is that 2/n?

Answer 2

this is not a problem that involves converting to a definite integral (the biggest give away being that there is no limiting process, e.g. \(n\to\infty\)). it's purely a series simplification problem:
$$\sum_{k=0}^4(3k+3)$$you can manually evaluate \(3k+3\) for \(k=0,\dots,4\) and sum or you can use properties of summation to simplify:$$\sum_{k=0}^4(3k+3)=3\cdot\sum_{k=0}^4k+\sum_{k=0}^4 3$$these sums are a little easier to swallow, since the first is \(0+1+2+3+4=10\) while the latter is \(3+3+3+3+3=3\cdot5=15\) hence $$\sum_{k=0}^4(3k+3)=3\cdot10+15=45$$

Answer 3

Ahhhh thank you, i was looking at this from the wrong direction