University⏱ 4 min

Power Series

Series of the form Σ aₙ xⁿ

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eˣP3(x)
Number of terms: 4
ex=x00!+x11!+x22!+x33!e^x = \frac{x^{0}}{0!}+\frac{x^{1}}{1!}+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}

Power series express functions as infinite polynomials. Each added term improves the approximation. For eˣ convergence is perfect everywhere.