MacLaurin Series
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Last updated 4:41 PM on 4/15/26
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7 Terms
1
New cards
1/1-x
1+x+x²....+x^n+...
= ∑xⁿ
(|x|<1)
2
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1/1+x
1-x+x² ....+(-x)ⁿ+...
= ∑(-1)ⁿ*xⁿ
(|x|<1)
3
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e^x
1+x+x²/2!+x³/3!....+xⁿ/n!+...
= ∑xⁿ/n!
(for all real x)
4
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sinx
x-x³/3!+x⁵/5!....((-1)ⁿ)x²ⁿ+¹/(2n+1)!+...
= ∑((-1)ⁿ)x²ⁿ+¹/(2n+1)!
(for all real x)
5
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cosx
1-x²/2!+x⁴/4!....+((-1)ⁿ)x²ⁿ/(2n)!
= ∑((-1)ⁿ)x²ⁿ/(2n)!
(for all real x)
6
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ln(1+x)
x-x²/2+x³/3....+(-1)ⁿ⁻¹xⁿ/n+...
= ∑((-1)ⁿ⁻¹)xⁿ/n
(-1
7
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arctan(x)
x-x³/3+x⁵/5.....(-1)ⁿx²ⁿ⁺¹/(2n+1)+...
= ∑((-1)ⁿ)x²ⁿ⁺₁/(2n+1)
(|x| ≤ 1)