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What does the Nth term test test for?
divergence
How do you know a series will diverge (nth)
The limit as a approaches infinity is not 0
What will happen if r<1 (geometric)
series converges
What will happen if r>1 (geometric)
diverges
Sum of a series
S = a/(1-r)
n is in the exponent
geometric series
n is in the base
p-series
What will happen if p<1 (p-series)
diverges
What will happen if p>1 (p-series)
converges
Convergence for a p-series
(1/(p-1)) < C < (1 + (1/(p-1)))
Limitations for integral test
function must be decreasing