summation methods Flashcards
geometric series sum of (A/B)^n
(A/B n=1)/(1-(A/B)
MUST BE -1<(A/B)<1 or else it diverges
Telescoping 1/factorable
a/factor +b/factor
find a and b, factor out if needed and then. plug in numbers cancel out
DIF BETWEEN FACTORS IS # OF FRACTIONS THAT DONT CANCEL
p-series 1/n^p
if p > 1 CONVERGES
if p ≤ 1 DIVERGES
if not geometric telescoping or p-series what do you do?
determine if the lim n->infinity of the function is = zero
if lim n->inifinity of the function does not equal 0 then what?
DIVERGES by nth term test
if lim n->inifinity of the function does equal 0 and it does look like a geometric telescoping or p-series then what?
use DCT or LCT
if lim n->inifinity of the function does equal 0 and it does not look like a geometric telescoping or p-series then what?
integral test
Integral Test
take the function turn it into an integral and do limit (antideriv) to see if it sdiverges or converges
Direct Comparison Test (DCT)
cancel out anything and compare to a new summation.
if new summation is GREATER and CONVERGES than our summation also CONVERGES
if summation is LESS THAN and DIVERGES than our summation also CONVERGES
Limit Comparison Test (LCT)
cancel out anything and compare to a new summation.
take the limit of your summation/new summation
if a finite and pos # then both converge or both diverge
if =0 and new sum converge then CONVERGE
if infinity and new sum diverge then DIVERGE
IVT Theorm
if the function on the interval and f(c) is inside that interval that value must exist
lim x-> infinity Cx^a / Dx^b
a>b pos or neg infinity
a=b C/D
a<b 0
tangent line
y=f(a)+f’(a)*(x-a)
nondifferentiable
cusp, vertical tangent line, discontinuity
deriv of tan x
sec^2 x
