Sequence23 (2 points)

We define the following mathematical series:

\[\begin{split}& x_0 = 0.5 \\ & x_i = \frac{1}{i^2 \sqrt{i}} + x_{i-1}, \quad i>0 \\\end{split}\]

Write function sequence23() that takes two values, k and eps (both float) and returns the summation (float) of the terms of this series until we reach the first term which is equal to k with a tolerance eps. This term will not be included in the summation. We say that two values, \(a\), \(b\) are equal with a tolerance \(\epsilon\) when they meet the following condition: \(abs(a-b) < \epsilon\)

Save this function in file sequence23.py.

Examples:

>>> round(sequence23(0.5, 0.1), 2)
0.0
>>> round(sequence23(1.5, 0.1), 1)
0.5
>>> round(sequence23(1.77, 0.01), 3)
5.418

Note

More tests are provided in file test-sequence23.txt.