I'm having some issues trying to understand a problem. I think that what makes me confused is that we have to put the k+1 in the exponent of a fraction, at the beginning of the induction step, where k=k+1. From that point on I'm not really sure how to continue with this proof.
Here's the problem at issue:
Use mathematical induction on $n$ to prove that $\forall n \in \mathbb{N}$: $$ \sum_{i=1}^n \left( \frac{1}{3} \right)^i = \frac{1}{2} \cdot \frac{3^n -1}{3^n} $$
Can anybody give me a hand?
Thanks in advance!