Expert: Paul Klarreich - 2/7/2009

Question
Prove that 2^n does not converge to any limit.

Answer
Questioner:   Husneara
Category:  Calculus
Private:  No
 
Subject:  limits
Question:  Prove that 2^n does not converge to any limit.
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I am not completely sure you are serious about this, but I will assume you are and that you need a rigorous proof.

Given X > 0, let N = ceil(log[2](X))

[Notation: that is the smallest integer that is not smaller than the base-2 logarithm of X.)

Then if  n > N, 2^n >= X.

That should do it.