Chapter 5.6, Problem 373E

For which values of r>0. if any, does ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}{r}^{\sqrt{n}}}$

converge? (Him: ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}{a}_n={\displaystyle \underset{k=1}{\overset{\infty }{\sum }}{\displaystyle \underset{n=k^2}{\overset{{\left(k+1\right)}^2-1}{\sum }}{a}_n}}}$)