What are common mistakes students make with infinite series?
I think the most common mistake people make with these is trying to find the sum when the common ratio is greater than or equal to 1. The common ratio must be less than 1 for the graph to converge at a sum. If it's equal to or greater than 1, the series diverges and will have no sum. It's very easy to forget this, though, and I wouldn't be surprised if some students get problems wrong because of this.