Find the value of Sum((1/2)^n*sqrt(2^(n-1)))

Will give best answer if someone can show me how to do it step by step. The sum is from 1 to infinity. Thanks in advance, much appreciated.

I assume the square root term is not part of the exponent, i.e.
Sum( ((1/2)^n) * sqrt(2^(n-1)) )

First thing is to manipulate it so it has a single n term
= Sum( (2^(-n)) * 2^((n-1)/2) )
= Sum( 2^(-n + (n-1)/2))
= 2^(-1/2) * Sum( 2^(-n + n/2))
= 2^(-1/2) * Sum( 2^(-n/2))

Now. see if we can get this so that the power is always n:
= 2^(-1/2) * Sum( (1/sqrt(2))^n)

Now that's the form of a geometric series, so you can use the formula
Sum(r^n) = 1 / (1-r)
if |r| < 1, which it is in this case

=> sum = 2^(-1/2) * (1 / (1 - 1/sqrt(2)))