Topics: Calculus - Sequence - Limit


Let be a sequence and .

We say that is the limit of when tends to infinity if , such that if .

This is denoted by:

When a sequence has a limit, we say that it converges. When it doesn’t, then we say it diverges.

Limits of sequences can be operated.

Limit of a Sum of Sequences


Let be sequences such that and .

Then, the sequence converges and .

Limit of a Sequence Greater than 0


If and is convergent, then:

Sandwich Limit


If , , are convergent sequences such that:


(we can prove this theorem with the previous theroem)