Calculus 2 - Important Maclaurin Series & Invercals of Convergence

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10 Terms

1
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1/(x-1) = Σ ∞k=0 xk = 1 + x + x2 + x3 + …

1/(x-1), -1 < x < 1

2
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1/(x2+x) = Σ ∞k=0 (-1)kx2k = 1 - x2 + x4 - x6 + …

1/(x2+x), -1 < x < 1

3
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ex = Σ ∞k=0 xk/k! = 1 + x + x2/2! + x3/3! + x4/4! + …

ex, -∞ < x < +∞

4
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sin(x) = Σ ∞k=0 (-1)k (x2k+1)/(2k+1)! = x - x3/3! + x5/5! - x7/7! + …

sin(x), -∞ < x < +∞

5
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cos(x) = Σ ∞k=0 (-1)k (x2k)/(2k)! = 1 - x2/2! + x4/4! - x6/6! + …

cos(x), -∞ < x < +∞

6
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ln(1 + x) = Σ ∞k=1 (-1)k+1 (xk)/k = x - x2/2 + x3/3 - x4/4 + …

ln(1 + x), -1 < x =< 1

7
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tan-1(x) = Σ ∞k=0 (-1)k (x2k+1)/(2k+1) = x - x3/3 + x5/5 - x7/7 + …

tan-1(x), -1 =< x =< 1

8
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sinh(x) = Σ ∞k=0 (x2k+1)/(2k+1)! = x + x3/3! + x5/5! + x7/7! + …

sinh(x), -∞ < x < +∞

9
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cosh(x) = Σ ∞k=0 (x2k)/(2k)! = 1 + x2/2! + x4/4! + x6/6! + …

cosh(x), -∞ < x < +∞

10
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(1 + x)m = 1 + Σ