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.
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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. |
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