1. If a sequence has the limit , then we can say that:
n →
If the limit is finite, then it is convergent. Otherwise, it is divergent.
2. If the limit of the sequences {} and {} are finite and is constant, then we can say that
i) n → n → n → .
ii) n → n → n → .
iii) n → n → .
iv) n → n → n → .
v) n → n → n →.
3. If and n → n → , then n → .
4.if n → , then n → as well.
5. We say that:
![Introduction to sequences](https://dcvp84mxptlac.cloudfront.net/diagrams2/CALC2-5-1-X.png)
Where the sequence {} is convergent for -1< 1, and divergent if > 1.