Infinite sequences are lists of numbers that go on forever.
You can define them in different ways, often using a formula.
For example, the sequence (a_n = \frac{1}{n}) includes numbers like (1), (\frac{1}{2}), (\frac{1}{3}), and so on.
As (n) gets larger, the numbers in this sequence get closer and closer to (0).
Now, let’s talk about series.
A series is simply the sum of the numbers from an infinite sequence.
For the sequence (a_n = \frac{1}{n}), the series looks like this: (S = 1 + \frac{1}{2} + \frac{1}{3} + ...)
This series is called a divergent series.
That means it keeps increasing without ever stopping.
Understanding how sequences and series work is really important in math, especially in a branch called calculus.
In calculus, we often focus on whether or not a series converges, meaning whether it approaches a specific value or not.
Infinite sequences are lists of numbers that go on forever.
You can define them in different ways, often using a formula.
For example, the sequence (a_n = \frac{1}{n}) includes numbers like (1), (\frac{1}{2}), (\frac{1}{3}), and so on.
As (n) gets larger, the numbers in this sequence get closer and closer to (0).
Now, let’s talk about series.
A series is simply the sum of the numbers from an infinite sequence.
For the sequence (a_n = \frac{1}{n}), the series looks like this: (S = 1 + \frac{1}{2} + \frac{1}{3} + ...)
This series is called a divergent series.
That means it keeps increasing without ever stopping.
Understanding how sequences and series work is really important in math, especially in a branch called calculus.
In calculus, we often focus on whether or not a series converges, meaning whether it approaches a specific value or not.