Combination_Theorem_for_Sequences_Real

Let $\sequence {x_n}$ and $\sequence {y_n}$ be sequences in $\R$. Let $\sequence {x_n}$ and $\sequence {y_n}$ be convergent to the following limits $\displaystyle \lim_{n \mathop \to \infty} x_n = l$ $\displaystyle \lim_{n \mathop \to \infty} y_n = m$ Let $\lambda, \mu \in \R$. Then the following results hold === Sum Rule === === Difference Rule === === Multiple Rule === === Combined Sum Rule === === Product Rule === === Quotient Rule ===