# Math Help - Power series

1. ## Power series

a_nx^n, b_nx^n are two power series with radius of convergence R1, R2, respectively.
If R1 is different than R2, how can i prove that the radius of convergence of the power series (a_n + b_n)x^n is min{R1, R2}?
And what can be said about the radius of cenvergence if R1=R2?

Thanks for any help

2. since the center is 0 for both 'series'
I would like to see a sum here
the sum of the two series is convergent for all x between $\left(-\min\{R1,R2\},\min\{R1,R2\}\right)$