Radius of Convergence for Polynomial I have to find the radius of convergence for this one, but I haven&rsquo;t found a solution for this type of a term.

$\mathbb f (x)$ = $1 + 7x^3 + 5x^4 + x^{13} + x^{2015}$

Could you help me out?
Being a finite sum, this one converges for every $x \in \Bbb C$, so its radius of convergence is $\infty$.
Pardon the bad English, but I struggle with this to and the comment above doesn't helped me to totally demonstrate the situation, so here is a more complete answer to anyone who has to demonstrate the radius of convergence for a polynomial.
What happens to the nth derivative of your function when n is greater than one plus your biggest exponent? all are 0.
So, you can write the polynomial as your polynomial plus the sum from 0 to infinity of your nth derivative of your function over n factorial times $(x-a)^n$ where a is your center.
Since the nth derivative at this point are all equal, you're multiplying a constant, so you can bring to the outside of the sum that constant (property of sums) and now you can make any test to show that the radius of convergence is infinite.