How to calculate the sum of the sequence without using built-in functions for exponentiation?

Question

I need to calculate the sum of the sequence in Python but I can't use the built-in functions for exponentiation.

It means I can't use ** and pow(). I have to create my own function for that.

So I created the function for exponentiation but it works only for numbers. I need to calculate my formula to the nth.

My function for exponentiation:

def exponentiation(a,b):
    result = 1
    for index in range(b):
        result = result * a
    return result

For numbers, it works. But when I want to do this to the nth (I defined 'n' as a Symbol) I get:

'Symbol' object cannot be interpreted as an integer

So I don't know how to fix that.

And if I want to calculate the sum of the sequence, I use and it works:

sy.summation((-1/2)**n, (n,1, oo))

But as I said before I need to change ** to my own exponentiation function, but it still shows that 'Symbol' object cannot be interpreted as an integer.

sy.summation(exponentiation((-1/2),n), (n,1, oo))

Do you have any advice?

Answer 1

The 'nth' means any given number. So you don't need to (and I can't think how you would) exponentiate any symbols. I think you can maybe simplify things a bit, if you return a list instead of just the nth value:

def exponentiation(a, n):
    result = 1
    exponents_list = []
    for i in range(n):
        result *= a
        exponents_list.append(result)
    return exponents_list

then work with the list with a for loop to get your sum

if you have to work with sympy, check this answer: Summation over a sympy Array