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Taylor series for 1/x about x=1,
∑ₙ₌₀^∞ (−1)ⁿ(x−1)ⁿ
Taylor series for ln x about x=1,
∑ₙ₌₁^∞ (−1)ⁿ⁻¹(x−1)ⁿ / n
Maclaurin series for ln(1+x),
∑ₙ₌₁^∞ (−1)ⁿ⁺¹ xⁿ / n
Maclaurin series for −ln(1−x),
∑ₙ₌₁^∞ xⁿ / n
Maclaurin series for sin x,
∑ₙ₌₀^∞ (−1)ⁿ x^(2n+1) / (2n+1)!
Maclaurin series for e^x,
∑ₙ₌₀^∞ xⁿ / n!
Maclaurin series for cos x,
∑ₙ₌₀^∞ (−1)ⁿ x^(2n) / (2n)!
Maclaurin series for arctan x,
∑ₙ₌₀^∞ (−1)ⁿ x^(2n+1) / (2n+1)
Maclaurin series for 1/(1+x),
∑ₙ₌₀^∞ (−1)ⁿ xⁿ
Maclaurin series for 1/(1−x),
∑ₙ₌₀^∞ xⁿ