How will you approach for program that computes this function f(X) = f(X+1) + X?

Question

For input X=3 the program computes -2 as output and for X=4 the program computes -5. f(0) = 0
1 <= N <= 800

Answer 1

you didn't specified the base case, if its 3 then you can use recursion as Sonic answered, but if its for x=0(lets say) then also you can find f(0) easily & use it as base case :
f(x)=f(x+1)+x
let x=2 : f(2)=f(3)+2
=> f(2)=-2+2=0
let x=1 : f(1)=f(2)+1
=> f(1)= 0+ 1=1
let x=0 : f(0)=f(1)+0 =1

So using this we can find value if base case(here we found value of base case(x=0) as 1)

Answer 2

I think the function is better expressed as:
f(x+1)=f(x)-x
OR
f(x)=f(x-1)-x+1
Let your f(0) value be stored as A.
Then,
def f(x):
if x==0:return A
return f(x-1)-x+1

Or you can approach this from a mathematical approach. You don't need long to figure that
f(x)=A-x*(x-1)/2
or something like that which I don't know.

Answer 3

This way maybe ?

https://code.sololearn.com/cevMiKtMENGD/?ref=app

Answer 4

I would think:
f(x+1) = f(x) - x or
f(n) = f(n-1) - (n -1)
Use recursion. Not sure if your base case is f(3) = -2 or f(4) = -2.