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