given a power series S = $\sum (1+n+2^{n}) x^{n} $ we have to find the radius of convergence of the power series. If we use the fact that radius of convergence is limit of the the sequence $ \frac {a_n}{a_{n+1}} $ as n tends to $ \infty $ I am getting the radius of convergence to be = $\frac{1}{2}$ could someone please guide me if I am right or wrong and consider posting a valid justification in each of the above scenario !
2026-04-03 21:46:18.1775252778
what is the radius of convergence of power series?
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$$2=\sqrt[n]{2^n} \leq \sqrt[n]{1+n+2^n} \leq \sqrt[n]{2^n+2^n+2^n}=2\sqrt[n]{3} \to 2$$