Given the geometric series
54 + 18 + 6 + ... + ... + 54(\frac{1}{3})^{n-1}
2.1 Show that the sum of the first n terms of the series is given by $81 - 81(\frac{1}{3})^n$
2.2 Calculate the smallest value of n for which the sum of the first n terms is greater than 80,99
2.3 What does $(\frac{1}{3})^n$ approach when $n \to \infty$?
2.4 Determine the value of $\sum_{k=1}^{\infty} (\frac{1}{3})^{k-1}$
