Python recursive zeno() function

Question

In python, I need to define a recursive function that takes a number a returns the sum 1/2^0 + 1/2^1 + 1/2^2 + 1/2^3 + ... + 1/2^n. I need to accomplish this without using a for or while loop. This is what i have tried.

def zeno(n):
    if n==0:
        return 1/1
    else:
        return float(1/1 + 1/2**zeno(n-1))

Answer 1

def zeno(n):
    if n==0: 
        return 1 #return 1 for base n==0 case, x ^ 0 is always 1
    else:
        return 0.5**n + zeno(n-1)  #calculate (1/2) ^ n + (1/2)^(n-1) recursively