The number e from a sequence

You will write three functions that explore $\left(1 + \dfrac{k}{n}\right)^n$ by computer. The checker compares them with $e^k$.

The idea. For large $n$ the value $\left(1 + \dfrac{k}{n}\right)^n$ is close to $e^k$. How large must $n$ be for the difference to be small? You try $n = 10, 100, 1000, \dots$ until it is.

Your tasks.

1. Finish compound(n). Return $\left(1 + \dfrac{1}{n}\right)^n$.
2. Finish power_form(k, n). Return $\left(1 + \dfrac{k}{n}\right)^n$.
3. Finish n_needed(k, tolerance). Try $n = 10, 100, 1000, \dots$ in order. Return the first power of ten for which power_form(k, n) differs from math.exp(k) by less than tolerance.