Power Series 1 Over 1-x
- Page ID
- 90632
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 \(f(x) = \frac{1}{1-x}\).
\(S_0(x)=1\)
\(S_1(x)=1+x\)
\(S_2(x)=1+x+x^2\)
\(S_3(x)=1+x+x^2+x^3\)
\(S_4(x)=1+x+x^2+x^3+x^4\)
\(S_5(x)=1+x+x^2+x^3+x^4+x^5\)
\(S_6(x)=1+x+x^2+x^3+x^4+x^5+x^6\)
\(S_7(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7\)
\(S_8(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8\)
\(S_9(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9\)
\(S_{10}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}\)
\(S_{11}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}\)
\(S_{12}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}\)
\(S_{13}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}\)
\(S_{14}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}\)
\(S_{15}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}+x^{15}\)
\(S_{16}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}+x^{15}+x^{16}\)
\(S_{17}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}+x^{15}+x^{16}+x^{17}\)
\(S_{18}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}+x^{15}+x^{16}+x^{17}+x^{18}\)
\(S_{19}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}+x^{15}+x^{16}+x^{17}+x^{18}+x^{19}\)
\(S_{20}(x)=1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^{10}+x^{11}+x^{12}+x^{13}+x^{14}+x^{15}+x^{16}+x^{17}+x^{18}+x^{19}+x^{20}\)