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### Section 10.14 : Power Series

For each of the following power series determine the interval and radius of convergence.

1. $$\displaystyle \sum\limits_{n = 0}^\infty {\frac{1}{{{{\left( { - 3} \right)}^{2 + n}}\left( {{n^2} + 1} \right)}}{{\left( {4x - 12} \right)}^n}}$$ Solution
2. $$\displaystyle \sum\limits_{n = 0}^\infty {\frac{{{n^{2n + 1}}}}{{{4^{3n}}}}{{\left( {2x + 17} \right)}^n}}$$ Solution
3. $$\displaystyle \sum\limits_{n = 0}^\infty {\frac{{n + 1}}{{\left( {2n + 1} \right)!}}{{\left( {x - 2} \right)}^n}}$$ Solution
4. $$\displaystyle \sum\limits_{n = 0}^\infty {\frac{{{4^{1 + 2n}}}}{{{5^{n + 1}}}}{{\left( {x + 3} \right)}^n}}$$ Solution
5. $$\displaystyle \sum\limits_{n = 1}^\infty {\frac{{{6^n}}}{n}\,{{\left( {4x - 1} \right)}^{n - 1}}}$$ Solution