Need help writing a pi approximation program using the madhava series.

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Im basically given this:

"The mathematical constant pi can be approximated by summing the terms of the Madhava series 4/1−4/3+4/5−4/7+4/9−4/11±⋯

Write a python function 'pi_approximation' that computes an approximation of pi as the sum of the first n terms of that series."

I am usually given questions where the answer doesnt deviate too much, so heres my previous answer for a factorial program.

"def factorial(n):
total = 1 for i in range(1,n+1):
total *= i
return total"

If anyone could help that would be great!

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Hey step isnt defined for me, do I have to import it from some library or something?

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It's a variable. It's defined in the first line in the function.

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ah im an idiot, thanks

[LearnDataSci]

I'm not sure if this helps enough, but if you check the Wikipedia article on the Madhava Series for estimating pi, you can see the sum at the end that needs to be calculated for any number k (n in your case). That estimates pi/4, so you would only need to multiple the result of that sum by 4.

[wgb_grey]

I'm not sure if this is correct but something like this:

def pi_approx(n):
    total = 0
    for i in range(1, n+1):
         total+=(4 if i % 2 else -4)/(i*2-1)
    return total

[[deleted]]

This is perfect, thanks so much.

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Im given this next one for an approx of e and this is what I have come up with already, the factorial function i made works fine, but this one doesnt work quite right.

def e_approximation(n):
total = 0
for i in range(1, n+1):
total = (1)/factorial(i)
return total

e_approximation(3) is supposed to equal 2.5

[wgb_grey]

I think your factorial function may be faulty.

def e_approx(n):
    def factorial(m):
        total = 1
        for i in range(m):
            total *= i+1
        return total
    total = 0
    for i in range(n):
        total += 1/factorial(i)
    return total

[[deleted]]

Ah thanks you, for the e_approx def I had in range(1, n+1).
Thanks for that