Could someone show me how to solve the following limits algebraically:
For x > 1, lim as n approaches infinity of
a) [(1 + x^(1/n))/2]^(2n) = x
b) [(1 + x^(1/n))/2]^(n) = sqrt(x)
They seem very similar to the sequence (1 + (a/n))^n whose limit is e^a, but I don't see how to manipulate it accordingly.
If you could show me how to solve these, I would really appreciate it.
Thanks in advance.