Series Study Review

Question 1

nth term test

Answer 1

if the limit as An approaches infinity does NOT = 0, then the sum of An diverges

Question 2

geometric

Answer 2

if |r| < 1, then the series converges
if |r| >= 1, the the series diverges

to find the sum A/(1-r)

Question 3

integral

Answer 3

Take the integral to find convergence or divergence, but not the sum

Question 4

telescoping

Answer 4

Think PFD, factor it, then sub write the sum out until the next number will be cancelled out down the line.

Question 5

p-series

Answer 5

ex: 1/n^p

if p > 1, the series converges
if p < 1, the series diverges

Question 6

alternating series test

Answer 6

an alternating series converges if:

the limit as n approaches infinity = 0
it’s decreasing

Question 7

Comparison (direct)

Answer 7

My hunch is it either converges or diverges

Diverges: the original series function > the new series function
Converges: the original series function < the new series function

Question 8

Comparison (limit)

Answer 8

Find a “similar” series
Calculate the limit of An/Bn
If the limit is finite the series will do the same thing

Question 9

ratio

Answer 9

Use if there’s a factorial (ex: 3!)

If the limit of the series is > 1, it converges
if the limit of the series is = 1, it’s inconclusive
if the limit of the series is < 1, it diverges

Sub (n+1) in for all n’s in the original series function, then multiply it by its original series function’s reciprocal.