If #sum c_nx_n# has a radius of convergence of #10# and #sum d_nx_n # has a radius of convergence of #11#, then what is radius of convergence of #sum (c_n + d_n)x_n#?
1 Answer
Mar 16, 2017
radius of convergence is
Explanation:
We have:
# sum(c_n+d_n)x_n = sum(c_nx_n+d_nx_n)#
# " " = sum(c_nx_n)+sum(d_nx_n)#
The 1st sum has radius of convergence 10
The 2nd sum has radius of convergence 11
So clearly both will converge if we look ta the intersection of the radii of convergence , ie sum has radius of convergence
