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.