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Convergence and limits

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Show that the following sequences are not convergent

i) (2^n)
ii) (((-1)^(n))n^2))
that is negative 1 to the n times n squared

Show that if X(sub n) is greater than or equal to zero for all n element N and lim(X(sub n))=0 then the lim(sqrtX(sub n))=0

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Solution Summary

This provides an example of proving sequences are not convergent and working with limits.

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Problem #1
(a) 2^n is convergent
For any positive number N, we can find the integer n > (log_2 N), then 2^n > 2^(log_2 N) = N.
Therefore, 2^n is convergent.
(b) (-1)^n * ...

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