You can use Sage to easily find the partial sums of an infinite series. Here is an example that adds the first 100 terms of the Harmonic series: \(1+ \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{100}\).
Here is a quick explanation of the code above.
Make a list of the terms in the series:
[1/n for n in range(1,101)]
Notice that the command range(1,101)
tells Sage to use the numbers from 1 up to 101, but not including 101! Sage is based on the Python programming language, and that is just how the range function works in Python.
Use the sum()
function to add up the terms in the series:
sum([1/n for n in range(1,101)])
This works, but Sage gives us the exact answer which is a fraction. That isn't really what we want, so we need one more step.
Convert the fraction to a decimal using the function N()
:
N(sum([1/n for n in range(1,101)]))
That's it! Feel free to adjust the code above on any homework problems that asks you to compute a partial sum.