calc final study

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Last updated 9:59 PM on 4/23/26
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9 Terms

1
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derivative of a power series

nan(x-c)n-1

2
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integral of a power series

an(x-c)n+1 / n+1

3
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1/1-x

∑xn = 1+x+x2+x3+…. R=1

4
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ex

∑ xn/n! = 1 + x/1! + x2/2! + x3/3! + …. R=∞

5
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sinx

∑(-1)n x2n+1 / (2n+1)! = x - x3/3! + x5/5! - x7/7! + …. R=∞

6
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cosx

∑(-1)n x2n/(2n)! = 1 - x2/2! + x4/4! - x6/6! + …. R=∞

7
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tan-1x

∑(-1)n x2n+1/2n+1 = x - x3/3 + x5/5 - x7/7 + … R=1

8
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ln(1+x)

∑(-1)n-1 xn/n = x - x2/2 + x3/3 - x4/4 + … R=1

9
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(1+x)k

∑(k n)xn = 1 + kx + k(k-1)/2! x2 + k(k-1)(k-2)/3! * x3 + …. R=1