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Power Serieshard
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Let f(x)=∑n=0∞anxnf(x) = \sum_{n=0}^{\infty} a_n x^nf(x)=∑n=0∞​an​xn be a power series with a finite radius of convergence RRR. If ana_nan​ satisfies the relation an=an−1⋅n2+1n2+na_{n} = a_{n-1} \cdot \frac{n^2 + 1}{n^2 + n}an​=an−1​⋅n2+nn2+1​, which of the following is the correct radius of convergence RRR for this series?