Find the radius of convergence of the power series where, $a_n= 2^n+3^n, n \geq 1$. The answer is given to be 1.
The tests I can use are Cauchy Hadamard Test and Ratio Test.
My attempt: Using Ratio Test:
$a_{n+1}= 2^{n+1}+3^{n+1}$,
which is giving me $|\frac{a_{n+1}}{a_n}|= \frac {\frac{1}{3} (\frac{2}{3}+(\frac{3}{2})^n)}{1+(\frac{3}{2})^n}$
So I'm not going anywhere in this method.
Using Cauchy Hadamard, I failed to find the limsup. Please help!