312 Rules (Sequence)
by EngliSea on 2020-07-14
Suppose that 「aₙ」 and 「bₙ」 are convergent sequences with limits A and B respectively; then the following rules apply:

❶ Sum rule
「aₙ+bₙ」 converges to A+B.

❷ Product rule
「aₙ·bₙ」 converges to A·B.

❸ Quotient rule
「aₙ/bₙ」 converges to A/B, provided that bₙ≠0 for each n and B≠0.

❹ Scalar product rule
「k·aₙ」 converges to k·A for every real number k.