Terms and sums of a GP

Write the formulas of a geometric progression yourself, with exact fractions, and test them against plain adding.

The idea. $a_n = ar^{n - 1}$, $S_n = \dfrac{a(r^n - 1)}{r - 1}$ for $r \ne 1$ and $na$ for $r = 1$, and $S_\infty = \dfrac{a}{1 - r}$ for $|r| < 1$.

Your tasks.

1. In nth_term, return $a r^{n - 1}$.
2. In gp_sum, return the sum of the first n terms by the formula. Handle r == 1 on its own.
3. In sum_to_infinity, return $\dfrac{a}{1 - r}$, or None when $|r| \ge 1$.