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 the series converges

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)