-1

  1. If radius of convergence of $\sum c_{n}x^{n}$ and $\sum d_{n}x^{n}$ is given say $a_{1}$ and $a_{2}$ respectively,then how can I find the radius of convergence of $\sum (c_{n}+d_{n})x^{n}$

  2. Given power series say $\sum_{n=0}^{\infty} a_{n}x^{n}$ has radius of convergence $R$,then what is the radius of convergence of $\sum a_{n}^{m}x^{n}$,$m$ is positive integer.

gt6989b
  • 54,422
ogirkar
  • 2,681
  • 14
  • 27
  • https://math.stackexchange.com/questions/309466/radius-of-convergence-of-a-sum-of-power-series This post partially answers your first question. – Lorenzo Riva Nov 27 '17 at 19:44
  • You can lose the privilege of asking questions, omkar, if you continue posting low quality questions. So please take suggestions in comments and improve your posts. This is not a "do my work for me" site. – amWhy Nov 28 '17 at 01:10
  • Ask one question only, per post, – amWhy Nov 28 '17 at 01:11
  • Sorry..I will keep this in mind for future..but seriously, I have lots of respect for this site and I have never use for such homework purpose.. – ogirkar Nov 28 '17 at 18:45

1 Answers1

0

**just a hint **

Let $a=\min (a_1,a_2). $

if $|x|<a $ then $\sum (c_n+d_n)x^n $ converges .

for the second, the ratio $\frac {a_n^m}{a_{n+1}^m} $ goes to $R^m $ if $R $ is the radius of $\sum a_nx^n $.

hamam_Abdallah
  • 62,951