Question

If 'x' is the level of the killed hero, the amount of experience gained is:
f(x) = f(x-1) + 20x; f(0) = 220;
What is the experienced gained if the killed hero is level 5?

Answer 1

We can do this recursively. Start by finding what f(1) is. Since you know what f(0) is, you can calculate f(1) by plugging in 1 for x and substituting f(0).

Answer 2

\[
\begin{split}
f(x) &= f(x-1)+20x\\
&= (f(x-2)+20x)+20x\\
&= f(x-2)+2\cdot 20x \\
&=f(x-x) +x\cdot 20x\\
&=f(0) + 20x^2\\
f(x) &= 20x^2+220
\end{split}
\]

Answer 3

ok

Answer 4

Hold on, what I did was not quite correct though.

Answer 5

Since I should have put \(f(x-1)=f(x-2)+20(x-1)\).

Answer 6

So \[
\begin{split}
f(x) &= f(x-n) + 20x\sum_{k=1}^{n}x+1-k\\
&=f(x-n) +20x\left(n(x+1)+\frac{n(n+1)}{2}\right)
\end{split}
\]

Answer 7

This is a bit trickier, so it may be easier to just it manually.\[
f(1) = f(0) + 20(1) = 220+20 = 240\\
f(2) = f(1) + 20(2) = 240+40 = 280\\
\dots
\]

Answer 8

ok thank you for all your help i appreciate it