Algebra of limits for sequences

Limits of sequences combine following the same rules valid for limits of functions.

Property — Algebra of limits for sequences

If $a_n\to a$ and $b_n\to b$ (both finite), then: $a_n + b_n \to a+b, \qquad a_n\cdot b_n \to a\cdot b, \qquad \frac{a_n}{b_n}\to\frac{a}{b}\ \text{(se }b\ne 0\text{)}.$

The indeterminate forms $\dfrac{0}{0}$, $\dfrac{\infty}{\infty}$, $\infty-\infty$, $0\cdot\infty$ require manipulations (hierarchy of infinities, factorisation, rationalisation, …) exactly as for limits of functions.

Links

Topics: Sequences
Concepts: Algebra of limits · Indeterminate form · Limit of a sequence
Skills: Compute limits