Post #10

Sequence:
take the limit to see if it diverges or converges
+if it has a limit it converges
+if you have a type of infinity it diverges

Finding terms: plug into equation
Partial Sums: add the term before it

Series:

Arithmetic sum: n(t+tn)/2
Geometric sum: t1/1-r

nth term test:
take the limit, may have to use L"H rule
+if you get zero must use different test
+if you get a number it diverges

Integral Test:
if you can integrate it easily
+if x is greater than or equal to one it converges
+anything else diverges

p-series test:
1/n^p
+if p is greater than 1 it converges
+if it is less than or equal to 1 it diverges

Geometric:
+if absolute value of r is less than 1 it converges
+greater than or equal to one it diverges

direct comparison test:
compare it to something easier
you then might get a geometric or p-series
use the test that works
+if you get it converges, stop
+if it diverges you must know ?

Limit Comparison Test:
compare to something easier
use another test
+divide original by compared
+take limit, if +ve number it converges
+if infinity, it diverges

alternating series:
will have like (-1)^n+1
+take the alternating part out for new
+take limit, must get zero
*if you get a number it diverges
+now add +1 to each n, less than or equal to, new one
+if true converges
+if not true diverges

Ratio Test:
usually used with ! or variable exponents
+add +1 to each n divided by the original
+things should cancel
* remember 2^n+1 can be written has 2^n 2^1 and (n+1)! is like n!(n+1)
+take limit
+less than 1 it converges, greater than 1 or infinity it diverges
+if you get one it is inconclusive

root test:
used when something is raised to the n
+take the nth root of the absolute value of the original
+take limit
+if you get less than 1 it converges, if you et greater than one or infinity it diverges
+if you get one it is inconclusive

Absolute Convergence: if absolute value of an converges then an converges
Conditional Convergence: if an converges but absolute vale does not converge