Power series for elementary functions

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6 Terms

1
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1/x

1 - (x - 1) + (x - 1)² - (x - 1)³ + … + (-1)^n(x - 1)^n + …

2
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1/(1+x)

1 - x + x² - x³ + … + (-1)^n x^n + …

3
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lnx

(x - 1) - (x - 1)²/2 + (x - 1)³/3 + … + (-1)^(n-1) (x - 1)^n/n + …

4
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e^x

1 + x + x²/2! + x³/3! + … + x^n/n! + …

5
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sinx

x - x³/3! + x^5/5! - x^7/7! + … + ((-1)^n x^(2n+1))/(2n + 1)!

6
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cosx

1 - x²/2! + x^4/4! - x^6/6! + … + ((-1)^n x^(2n))/(2n)!