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series

Geometric Series

|r|<1 , sum a/1-r

p-series

p>1

divergence

diverges: lim |an| ≠ 0

alternating series

lim = 0 & f(x)' is neg

absolutly convergent

|an| converges

conditionally convergent

|an| diverges but an converges

ratio test

lim |an+1/an| if < 1 it converges

doesnt work if = 1

root test

lim sq.root |an| if < 1 converges

1/n^3/2

p-series

1/(sq.root n) + 1

limit comparison

5n^2+3n+4/3n^2+7

divergence test

-n/3n+7

divergence test

2^3n(-9)^1-n

geometric

5^n3^1-n

geometric

3^2n(-11)^1-n

geometric

n^4+5n+1/3n^6+5

limit comparison

(-1)n+1/3n+1

alternating

n^3/n!

ratio

(n+2/ln(n^2+1))^n

root

1/(n+1)(n+2)

telescoping

telescoping

use partical fraction decomp. you will get a sum, meaning it will converge

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