Calculating linearly rising formula

Question

level = constant * sqrt(XP)

Level | XP | Difference

1 | 0 | -

2 | 100 | 100

3 | 300 | 200

4 | 600 | 300

5 | 1000 | 400

6 | 1500 | 500

7 | 2100 | 600

8 | 2800 | 700

9 | 3600 | 800

10 | 4500 | 900

Looking for an equation to calculate total exp needed for said level

for example, if I were to calculate total exp for level 10, it would be 16500

(0+100+300+600+1000+1500+2100+2800+3600+4500)

Answer 1

If we call "level" n, then XP=(n²-n)/2

and the sum of XP=(1/6)(n³-n)

This was derived from the calculus of finite differences.

If you need more education on this topic, try a reference by Jordan, "Calculus of Finite Differences".