ap calculus bc maclaurin series
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7 Terms
1
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1/1-x
1 + x + x² + … + xn +… = ∑ xn
(|x| < 1)
2
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1/1+x
1 - x + x² - … + (-1)n xn + … = ∑ (-1)n xn
(|x| < 1)
3
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ex
1 + x + x²/2! + … + xn/n! + … = ∑ xn/n!
(all real x)
4
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sin(x)
x - x³/3! + x5/5! - … = ∑ (-1)n[x2n+1/(2n + 1)!]
(all real x)
5
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cos(x)
1 - x²/2! + x4/4! - … = ∑ (-1)n[x2n/(2n)!]
(all real x)
6
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ln(1+x)
x - x²/2 + x³/3 - … + … = ∑ (-1)n-1(xn/n)
(-1 < x < 1)
7
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tan-1(x)
x - x³/3 + x5/5 - … + … = ∑ (-1)n[x2n+1/(2n + 1)]
(|x| < 1)