# The sum of two series is equal to $(\sum V_k.X^x)+(\sum H_k.X^x )=\sum (V_k+H_k)X^x$. Does this mean we can add their radius of convergence [closed]

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 $$1+2=3$$?

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