Math series Flashcards
arithmetic sequence recursively
An-1 + d
arithmetic sequence explicitly
a1 + (n-1)d
geometric sequence recursively
An-1 (r)
geometric sequence explicitly
a1 x r^n-1
geometric series
ar^n-1
geometric series test
absolute values
r>_1 diverges
r<1 converges a/1-r
harmonic series
sum 1/n
diverges
nth term test
take the limit
not 0: diverges
0: inconclusive
n in denominator
telescoping
partial fraction
then plug in, expand, cancels out
integral test
natural logs
An: continuous, positive, decreasing
limit w/ integral, switch to x
c if it diverges: series diverges
a number: converge
infinity: diverge
p-series test
1/n^p
p>1 converges
p
direct comparison test
choose a series(bn) bigger/smaller than the one given(an)
bn converge=an converge
an diverges=bn diverges
limit comparison
like limit
an/bn
pick bn
answer is bigger than 0
both an n bn does the same thing
answer is 0= converges if chosen converges
answer is infinity= diverges
alternating series
take limit of non alternating piece
if 0= converges, if not then diverges (absolutely)
converges absolutely: find sum of the series (w/o alternating piece) n it is convergent
alternating series estimation
sum of first 10 terms, the 11th term is how off the sum is from the real sum
sum is same sign as 11th term: underestimate
if not the same sign: overestimate
