Power Series with Real Variables

Tags: #math #power #series

Equation

$$e^{x}=1+x+\frac{x^{2}}{2!}+...+\frac{x^{n}}{n!}+... \\ \ln(1+x) = x - \frac{x^{2}}{2} + \frac{x^{3}}{3} + ... + (-1)^{n+1}\frac{x^{n}}{n!} +... \\ \cos(x) = \frac{e^{ix}+e^{-ix}}{2}=1-\frac{x^{2}}{2!}+\frac{x^{4}}{4!}-\frac{x^{6}}{6!}+...\\ \sin(x) = \frac{e^{ix}-e^{-ix}}{2i}=x-\frac{x^{3}}{3!}+\frac{x^{5}}{5!}+...$$

Latex Code

                                 e^{x}=1+x+\frac{x^{2}}{2!}+...+\frac{x^{n}}{n!}+... \\
\ln(1+x) = x - \frac{x^{2}}{2} + \frac{x^{3}}{3} + ... + (-1)^{n+1}\frac{x^{n}}{n!} +... \\
\cos(x) = \frac{e^{ix}+e^{-ix}}{2}=1-\frac{x^{2}}{2!}+\frac{x^{4}}{4!}-\frac{x^{6}}{6!}+...\\
\sin(x) = \frac{e^{ix}-e^{-ix}}{2i}=x-\frac{x^{3}}{3!}+\frac{x^{5}}{5!}+...

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Introduction


Explanation

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    2024-04-20 00:00

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    You can make it...
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    Anticipating a pass on this exam.
    2023-07-04 00:00

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    Best Wishes.
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