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9 Cards in this Set

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  • Back
  • 3rd side (hint)
Geometric Series
Summation 0 to infinity of a*r^k
Converges to a/(1-r) if abs(r)<1
kth Term Test
All series
if limit of asubk as k approaches infinity doesn't equal zero, it diverges
Integral Test
Summation from 1 to inf. of asubk where asubk is some continuous function of k, decr, and always greater than zero
the summation and the integral of f(k) on the same interval either both converge or both diverge
p-Series Test
The one with 1/k^p
Converges for p>1, diverges for p> or = 1
Comparison Test
you have 2 summations, where one nth term is always greater than the other
If the greater one converges, the lesser one converges. If the lesser one diverges, the great one diverges.
Limit Comparison Test
2 summations, both nth terms are greater than zero, and the limit of one over the other is greater than zero
Both Converge or both diverge
Absolute Convergence
Series with some positive and negative terms(including alternating series)
if abs of summation converges, then the summation converges absolutely
Ratio Test
Any series
limit as k approaches inf. of abs(asub(k+1)/asubk)
If it's less than 1 Converges
If it's greater than 1 Diverges
Root Test
Any series
kth root of abs of asubk