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Calculus/diverging sequence
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Hi, I'm stuck on a question about proving that a sequence does not converge to any limit. the sequence is 2^n. can u help me please??
Ok, first of all we do agree that : 2^n > n . It's easy to prove.
Now, the definition of a non converging sequence is :
For every N>0 , there exists M>0 such that : for every n>N, we get
|2^n|>M.
Let's apply our Lemma ( 2^n > n ) here :
2^n > n (& n >N) Thus 2^n>N. Therefore if we take M=N we get :
|a(n)|>(N=M) for every n>N. Q.E.D
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