Limits are really important when we talk about infinite series, but they can be tricky. Let’s break it down into simpler parts.

1. Understanding Convergence: An infinite series is when you keep adding numbers forever, like this: $S = a_1 + a_2 + a_3 + \ldots$. But not all of these series end up giving us a clear answer. Many students find it hard to tell when a series is getting close to a specific number or just keeps getting bigger and bigger without stopping.

2. Calculating Limits: Figuring out the limit of a series can be tough. There are different methods we can use, like the ratio test, root test, and comparison test. These can get pretty confusing, especially if you're not comfortable with sequences.

3. Implications of Divergence: If a series diverges, it means you can't assign a definite sum to it. This can be disappointing for students who wish to find a straightforward answer.

Even though these topics can be challenging, with some effort and practice, students can understand them better. By using convergence tests and working on limit calculations, you'll build your confidence and get better at dealing with infinite series!