Calc

Monotone

Always increasing or decreasing

Integral Test

Must be continuous, positive, and decreasing

When to use divergence test

Series has n = 1

When to use integral test

Series has easily integrated parts and compare to integral where it starts at n = 1

ln (a) - ln(b)

= ln(a/b)

How to estimate the value of a series

Using partial sums or convergence tests to approximate its limit.

Monotone Convergence Theorem

If a sequence is monotone (either non-decreasing or non-increasing) and bounded, then it converges.

How to use the squeeze theorem

To use the squeeze theorem, find two functions that 'squeeze' the function of interest between them. If the limits of both of these functions converge to the same value at a specific point, then the limit of the function of interest must also converge to that same value.

what is (n + 1)! equivalent to

(n+1) * n!

1/sqrt(n)

DIVERGES

sqrt(n)* sqrt(n) =

n

1/n

DIVERGES