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Having two power series $\sum V_k.X^k$ has a radius of convergence $1$ and another $\sum H_k.X^k$ with radius of convergence being $2$ and $(\sum V_k.X^k)+(\sum H_k.X^k)=\sum (V_k+H_k)X^k$... Can we conclude that

$$(\sum V_k.X^k)+(\sum H_k.X^k )=\sum (V_k+H_k)X^k$$

has the radius of convergence $1+2=3$?

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    $\begingroup$ Write in latex: \sum_{k}V_kX^{x}, enclosed with dollar signs. $\endgroup$ – vitamin d Feb 23 at 16:06
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    $\begingroup$ Does this answer your question? Radius of Convergence of Sum of two Series. $\endgroup$ – Elliot Yu Feb 23 at 16:10
  • $\begingroup$ We can conclude that the radius is greater or equal to $2$. For example, if $V_k = -H_k$, the radius is infinite. $\endgroup$ – Damien Feb 23 at 16:11
  • $\begingroup$ Thank you very much these comments were helpful $\endgroup$ – Leornard Feb 23 at 16:19