Fun with Power Series

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7 Terms

1
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ex

1 + x + x2/2! + x3/3! + ... + xn/n! (for all x)

2
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sin(x)

x - x3/3! + x5/5! - x7/7! + ... + (-1)n(x2n+1)/(2n+1)! (for all x)

3
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cos(x)

1 - x2/2! + x4/4! - x6/6! + ... + (-1)n(x2n)/(2n)! (for all x)

4
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1/x

1 - (x-1) + (x-1)2 - (x-1)3 + ... + (-1)n(x-1)n (for 0 < x < 2)

5
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ln(x)

(x-1) - (x-1)2/2 + (x-1)3/3 - ... + [(-1)n](x-1)n+1/n+1 (for 0 < x <= 2)

6
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1/1+x

1 - x + x2 - x3 + x4 + ... + (-1)n(xn) (for -1 < x < 1)

7
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arctan(x)

x - x3/3 + x5/5 - x7/7 + ... + (-1)n(x2n+1)/2n+1 (for -1 <= x <= 1)