Power series

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Problem: Expand function \( f(x)=e^{2 x} \) into a power series in the vicinity of the point \( x_{0}=3 \).

2.8.20 Power series

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Problem: Find the domain of convergence of the series: \[ \sum_{n=1}^{\infty} \frac{n x^{n}}{2^{n}} \text {. } \]

2.8.25 Power series

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Problem: Find the domain of convergence of the series: \[ \sum_{n=1}^{\infty} \frac{(x-1)^{n}}{n !} \]

2.8.26 Power series

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