Summation with power

Question

Please help me with the below Summation

$\sum_{r=0}^{\infty}2^r \times n^{\frac{1}{2^r}}$

While solving problem based on finding time complexity, I came upto this expression. I am unable to move further. Please help.

Answer 1

The infinite sum doesn’t converge:

$$\lim_{r \to \infty} 2^rn^{\frac{1}{2r}} = \lim_{r \to \infty} 2^r(1) = +\infty$$