math 1b midterm 2

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9 Terms

1
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taylor series

f^n(a)/n! * (x-a)^n

2
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taylor series expansion

f(a)+f’(a)/1! * (x-a)*^1 +f’’(a)/2! * (x-a)²

3
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taylor’s inequality

Rn(x)<= (Mn*(x-1)^(n+1))/(N+1)! <= (Mn*d^(N+1)/(N=1)!)

4
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Riemaan’s rearrangement theorem

the sum of any infinite series can be changed by rearranging the order of the terms if an is divergent

5
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n/n+1

1/(n+1)/n

6
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integral test conditions

positive, continuous, decreasing

7
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limit comparison test

if lim > 0, both diverge or converge

8
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ratio root tests

L=1 inconclusive, L<1 converge

9
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alternating series test

alternating, terms in an are decreasing, lim an =0