MathAnalysisCalculusLimits

Limits of sequences

The definition

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A number $A$ is the limit of the sequence $(a_{n})$ if and only if for any $\varepsilon > 0$ there exists $N$ such that...

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∣a_n​−A∣> \varepsilon

for any

n>N

∣a_n​−A∣< \varepsilon

for any

n>N

a_n​ - A < \varepsilon

for any

n>N

∣a_N​−A∣< \varepsilon

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