Understanding infinite sequences with math notation is really important for grasping how they work.

An infinite sequence is just a list of numbers that goes on forever. We usually name a sequence with a capital letter, like ( A ).

Notation

1. General term: We often use the symbol ( a_n ) to show the ( n )-th term of a sequence. Here, ( n ) is any positive whole number (1, 2, 3, and so on).

2. Set notation: We can write the sequence as ( {a_n}_{n=1}^{\infty} ). This tells us that we start listing the terms from ( n=1 ) and keep going forever.

Example

Let’s look at the sequence of even numbers. We can say it like this:

• ( a_n = 2n )

This means:

• For ( n=1 ), ( a_1=2 )
• For ( n=2 ), ( a_2=4 )
• For ( n=3 ), ( a_3=6 )
• And it keeps going...

By using math notation, we can neatly describe infinite sequences. This helps us understand their properties and how they behave.