Chapter 11 - Section 11.8 - Power Series - 11.8 Exercises - Page 752: 33

NO

For the interval of convergence $[0,\infty)$ we should have $a-R=0$ and $a+R=\infty$ which implies both $a=R=\infty$ Although we can have $R=\infty$ but $a\ne\infty$ Thus, we cannot have a power series with the interval of convergence $[0,\infty)$.