Question

Using python coding, test for convergence of an infinite sequence or series.

keep the coding at beginner level please!

Answer 1

I wrote up an example function that should work:

Σ (from n=1 to inf) (aⁿ )/(b^n-1) can be rewritten as Σ (from n=1 to inf) b*(a/b)ⁿ . Now that it's in this form, it's clear that this is a geometric series with r=(a/b). Thus, it will converge only when abs(a/b) < 1, and it will diverge otherwise. When it is in the divergent case, we will want to exit the function.

This is the function for it:

def compute_sum(a, b, tolerance=1e-5):
    if abs(a/b) >= 1:
        return None
    n = 1
    total_sum = 0
    prev_partial = 0
    while True:
        current_partial = b * (a / b)**n
        total_sum += current_partial
        if abs(prev_partial - current_partial) < tolerance:
            return total_sum
        prev_partial = current_partial
        n += 1        

As you can see, the first thing we do is check for divergence. I opted to return None in this case, but you can choose to throw an error if you'd like.

NOTE:Let me know if this answers your question or if I can explain anything better.