When do the different tests converge or diverge

When does geometric series converge and diverge

Converges when the r fraction in arⁿ is less than 1

or

Diverges when the r fraction in arⁿ is greater than or equal to 1

When does p-series converge or diverge

Converges when the exponent of the n in 1/n is greater than 1

or

Diverges when the exponent of the n in 1/n is less than or equal 1

When does integral test converge or diverge

If the integral of the series function exists, then the series converges

or

If the integral of the series function doesn’t exists, then the series diverges

When does divergence test converge or diverge

If the limit as n goes to infinity produces any number other than 0, then the series diverges

or

If the limit as n goes to infinity produces 0, then it is unknown

When does the alternating series test converge or diverge

Converges when b_n is decreasing.

Diverges when it is not

When does limit comparison test converge or diverge

If b_n converges, then a_n (the series) converges

or

If b_n diverges, then a_n (the series) diverges

How do you find the convergence point for geometric series’s

you use this formula

What 2 different functions are a_n and b_n used for

Alternating sequences a_n=(-1)ⁿb_n

and

Limit comparison test L=(a_n)/(b_n)

What does it mean to find the sum of a series

You just add up a bunch of terms to see what term it is approaching

Does this converge or diverge

it diverges because the -1 causes the values alternate. You can’t use the alternating series test because this is not a series.

What is the difference between finding the sum and finding the convergence of a sequence (not series)

Finding the sum is when you add up a bunch of terms starting at 0 and see what value it is getting closer to.

Finding the convergence of a sequence is when you list a bunch of values starting from 0

What do you have to do with the limit comparison test in addition to finding if a limit convergence test converges or diverges

You have to solve for a_n/b_n and it has to be greater than 0 and less than infinity