Power Series (Calc BC)

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8 Terms

1
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1/(1-x)

1 + x + x^2 + x^3 + x^4 + x^(n-1)+ ...

interval of (-1,1)

2
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1/(1+x)

1 - x + x^2 - x^3 + x^4 + ... (-1)^(n-1) x^(n-1) + ...

interval of (-1,1)

3
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1/(1+x^2)

1 - x^2 + x^4 - x^6 + ... (-1)^(n-1) x^(2n-2) + ...

interval of (-1,1)

4
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arctan x

x - x^3/3 + x^5/5 - x^7/7 + ... + ((-1)^(n-1) x^(2n-1) )/ (2n-1) + ...

Interval of convergence (-1, 1)

5
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e^x

1 + x/1! + x^2/2! + x^3/3! + x^4/4! + ... (x^(n-1))/ (n-1)! + ...

interval of convergence (-infinity, infinity)

6
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ln|x + 1|

x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ... ((-1)^(n-1) x^n)/n + ...

interval of convergence (-1, 1)

7
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sin x

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

interval of convergence (-infinity, infinity)

8
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cos x

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

interval of convergence (-infinity, infinity)