When creating a function with summation in it, how do you add terms to the summation? (Python)

I need to find a way to add new terms to the function:

f(x) = 4sin(x)/pi

such that the new function looks like this:

f(x) = 4sin(x)/pi + 4sin(3x)/3pi + 4sin(5x)/5pi + 4sin(7x)/7pi … up to 201.

I was thinking I could create the function with a for loop inside that would iterate using a list n but there must be a way to do it. I am using the math and numpy libraries. This is what I have so far:

# original function f(x)
def f(x):
     return (4/math.pi)*math.sin(x)

# create list (n) composed of odd numbers up to 201 
n = list(range(1, 202, 2))

# new function with added terms
def newf(x):
     for i in n:
          sum (4/n[i]*math.pi)*math.sin(n[i]*x)

I am still relatively new to Python and cannot find a similar example to troubleshoot with. Am I thinking through this correctly? I’m unsure why this code would not work.

I do not know how to do math notation in Stack Overflow, so I apologize for that!

Answer

You are close to the solution! The reason is not working is because inside your loop nothing is retaining the computation of the previous iterations. And you can simply use i without accessing n[i], which eventually will throw you an IndexError: list index out of range

The code should provide you what you need:

# original function f(x)
import math

def f(x):
     return (4/math.pi)*math.sin(x)

# create list (n) composed of odd numbers up to 201 
n = list(range(1, 202, 2))

def new_f(x):
    return sum([(4/i*math.pi)*math.sin(i*x) for i in n])