power series
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Last updated 5:44 PM on 3/22/26
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8 Terms
1
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\frac{1}{x}
\left(-1\right)^{n}\left(x-1\right)^{n}
IOC: (0,2)
2
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\frac{1}{1+x}
\left(-1\right)^{n}x^{n}
IOC: (-1,1)
3
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\ln x
\frac{\left(-1\right)^{n}\left(x-1\right)^{n}}{n}
IOC: (0, 2]
4
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e^{x}
\frac{x^{n}}{n!}
IOC: \left(-\infty,\infty\right)
5
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\sin x
\frac{\left(-1\right)^{n}x^{2n+1}}{\left(2n+1\right)!}
IOC: \left(-\infty,\infty\right)
6
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\cos x
\frac{\left(-1\right)^{n}x^{2n}}{\left(2n\right)!}
IOC: \left(-\infty,\infty\right)
7
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\arctan x
\frac{\left(-1\right)^{n}x^{2n+1}}{2n+1}
IOC: [ -1, 1 ]
8
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\arcsin x
\frac{\left(2n\right)!x^{2n+1}}{\left(2^{n}n!\right)^2\left(2n+1\right)}
IOC: ( -1, 1 ]
