MediumCalculusca-085

Arctan Series

Problem

Evaluate the Gregory series for arctan(x) to n terms:

arctan(x) ≈ sum from k = 0 to n-1 of (-1)^k * x^(2k+1) / (2k+1)

The series converges quickly for |x| < 1 but very slowly near x = 1, so partial sums there lag the true value.

Hint

Only odd powers appear; multiply the running power by x squared each step.

case 1

in: [0,5]

expected: 0

case 2

in: [0.5,20]

expected: 0.46364760900079693

case 3

in: [-0.5,20]

expected: -0.46364760900079693

case 4

in: [0.25,10]

expected: 0.24497866312685385

case 5

in: [1,10]

expected: 0.7604599047323508

Starter codePython

def arctan_series(x, n):
    # Your code here
    pass

5 test cases · run your code against them in the editor