Many students face confusion about sequences and series while learning calculus. Let’s clear up some common misunderstandings.

What Are Sequences and Series?
One big mistake is thinking that sequences and series mean the same thing.

A sequence is just a list of numbers in a certain order. For example, we could call it $a_n$.

On the other hand, a series is when you add up the numbers in a sequence. You can write it as $\sum_{n=1}^{\infty} a_n$.

It’s really important to know the difference between these two terms so you can understand calculus better.

Understanding Notation
Another thing that confuses students is the way we write these ideas.

The notation for sequences, like $a_n$, can look a lot like the way we write functions. But here’s the key: a sequence is a special kind of function that only works with whole numbers. This means the order of the terms matters, unlike regular functions.

What About Convergence?
Some students think that if a sequence doesn’t converge, then the series can't converge either.

This isn’t right. If a sequence does converge, that means the series made from its terms is likely getting close to a limit. But just because a series converges doesn’t mean the sequence has to.

Infinite Series Can Be Confusing
Finally, there’s confusion about infinite series.

Some students believe an infinite series automatically diverges just because it has an endless number of terms. However, that's not true! An infinite series can still converge. A good example of this is a geometric series when $|r| < 1$.

By addressing these misunderstandings, students can grasp sequences and series more easily, which will help them dive deeper into calculus!