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Power Series 1 Over 1-x

Last updated

May 30, 2024
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- Polar Conics
- Quadric Surfaces

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Visualize the Power Series Approximation of $f(x) = \frac{1}{1-x}$

Move the slider to see how well $\sum^N_{n=0}x^{n}$ approximates $f(x) = \frac{1}{1-x}$ .

N = 2

$S_0(x)=1$

$S_1(x)=1+x$

$S_2(x)=1+x+x^2$

$S_3(x)=1+x+x^2+x^3$

$S_4(x)=1+x+x^2+x^3+x^4$

$S_5(x)=1+x+x^2+x^3+x^4+x^5$

$S_6(x)=1+x+x^2+x^3+x^4+x^5+x^6$

$S_7(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7$

$S_8(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8$

$S_9(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9$

$S_{10}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}$

$S_{11}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}$

$S_{12}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}$

$S_{13}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}$

$S_{14}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}$

$S_{15}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}+x^{15}$

$S_{16}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}+x^{15}+x^{16}$

$S_{17}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}+x^{15}+x^{16}+x^{17}$

$S_{18}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}+x^{15}+x^{16}+x^{17}+x^{18}$

$S_{19}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}+x^{15}+x^{16}+x^{17}+x^{18}+x^{19}$

$S_{20}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}+x^{15}+x^{16}+x^{17}+x^{18}+x^{19}+x^{20}$

Visualize the Power Series Approximation of f(x)=11−xf(x) = \frac{1}{1-x}

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Visualize the Power Series Approximation of $f(x) = \frac{1}{1-x}$