Writing sums as functions: INTERACTIVE

We want to calculate the following general sum:

\[\sum_{k = 1}^{100} f(k) \]

where \(f\) is some function.

For the specific case \(f(k) = \frac{1}{k^2}\) we would be computing

\[\sum_{k = 1}^{100} \frac{1}{k^2} \]

and we could use the following code:

def my_sum(start, stop):
    """Sum the function 1/k^2 for integers between start and stop (inclusive)"""
    total = 0
    for k in range(start, stop + 1):
        total = total + (1 / k**2)
    return total

print(my_sum(1,100))

1.6349839001848923

But we could make this more general by allowing this to work on any function.

Let’s change this to accept an additional argument my_func

def my_sum(start, stop, my_func):
    """Sum the function 1/k^2 for integers between start and stop (inclusive)"""
    total = 0
    for k in range(start, stop + 1):
        total = total + my_func(k)
    return total

Now to call this we have to provide a start, a stop, and the form of \(f(k)\), my function. Of course, we are yet to define ```my_func``. So for \(f(k) = \frac{1}{k^2}\) we would do:

def my_func(k):
    """Return 1/k**2"""
    return 1/k**2

print(my_sum(1, 100, my_func))

1.6349839001848923

Putting this together: exercise

Using the above compute:

\[ \sum_{k=1}^{1000} \frac{1}{k^2}.\]

Exercise

Compute

\[ \sum_{k=5}^{75} k^3 - 7k^2 + k.\]