Proof: Constant Sequence Converges to its Constant Value | Real Analysis

Does a constant sequence converge? And if so, what does it converge to? As you'd expect, a constant sequence, where every term is equal to some real number c, converges to its constant value of c. We'll prove that constant sequences converge to their constant values in today's real analysis video lesson.

The math behind the proof is very simple. When we prove a sequence converges to a limit, we show that the sequence eventually gets within epsilon of its limit for any positive number epsilon. Of course, for our constant sequence equal to c at every term, it's always 0 away from c, since it is always equal to c, and so certainly c is its limit.

Real Analysis Playlist:   • Real Analysis  

Intro to Sequences:    • Intro to Sequences | Calculus, Real A...  
Definition of the Limit of a Sequence:    • Definition of the Limit of a Sequence...  

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