Limit of a sequence
Properties

Some other important properties of limits of real sequences include the following:

These properties are extensively used to prove limits, without the need to directly use the cumbersome formal definition. For example, once it is proven that 1 / n → 0 {\displaystyle 1/n\to 0}, it becomes easy to show—using the properties above—that a b + c n → a b {\displaystyle {\frac {a}{b+{\frac {c}{n}}}}\to {\frac {a}{b}}} (assuming that b ≠ 0 {\displaystyle b\neq 0}).
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