Math 2 series

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7 Terms

1
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Ratio Test

L<1 convergent, L=1= Inconclusive (use other test), L>1 or infinity Divergent

2
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Root Test

L<1 Convergent, L>1 Divergent, L=1 Inconclusive

3
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P series

p>1 Convergent, p≤1 Divergent

4
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Direct Comparsion test

Take out useless numbers
If bigger converges then smaller converges.
If smaller diverge them bigger diverge.
If backwards, it’s inconclusive

5
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Integral Test

The function has to be positive, continuous, & decreasing on the interval 0-infinity. If the integral equals a finite value, it converges; if it equals infinity, it diverges

6
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N-th term test

If lim n→∞ an=0 then it inconclusive; if not then it diverges

7
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Limit comparison test

If 0≤an & 0<bn & lim n→∞ =L
where 0<L
if bn converges then an will
& vice versa & same applies to diverge