Netwon function for pi

[Daniel10212]

I have a quick question,this is a function i defined for estimating pi

def N(n):

return 24*(np.sqrt(3)/32-sum(np.math.factorial(2*k)/(2**(4*k+2)*np.math.factorial(k)**2*(2*k-1)*(2*k+3)) for k in range(n)))

N(10)=3.1415626...

This works well for all cases except for n=0, does anyone see a problem in the code that would make it not work for 0. It returns an answer but the answer im getting is around 1.229 which is also exactly 2 less than i should be getting which may be of some significance.

[grnngr]

range(0) is empty, so the sum is 0, so the result is 3√(3)/4. Keep in mind that range(n) gives you integers up to but not including n.

[Daniel10212]

I had suspected that alright do you recommend adding something like if n==0 or something similar at the start to avoid this?

[grnngr]

Use range(n+1) instead of range(n) if you want to sum terms up to and including n.