Studied by 14 people
Which test should you always start with?
nth term test
lim n→∞ an=0
nth term test is inconclusive
lim n→∞ an doesn’t =0
inconclusive, use another test
1/n^p
p >1
series converges by p-series
1/n^p
p≤ 1
series diverges by p-series
∑a(r)ⁿ
|r|<1
series converges by geometric series
∑a(r)ⁿ
|r|≥1
series diverges by geometric series
which test should you use when you see ∑(an)ⁿ
root test
lim n→∞. ⁿ√|an| < 1
series converges by root test
lim n→∞. ⁿ√|an| > 1
series diverges by root test
which test should use you when you see factorials and exponentials
ratio test
lim n→∞ |an+1/an| < 1
series converges by ratio test
lim n→∞ |an+1/an| >1
series diverges by ratio test
when you see (-1)ⁿ
use alternating series test, if terms are dec in abs value towards 0
lim n→∞ |an| = 0
series converges by alt srs test
lim n→∞ |an| doesn’t = 0
doesn’t converge by alt srs, use nth term test to prove divergence
If you see a series where there would be a u-sub, use
integral test if the series is positive, cont, and dec
lim b→∞ ∫ from b to ∞. = #
series converges by integral test
lim b→∞ ∫ from b to ∞. = ∞
series diverges by integral test
If a series looks < or > a similar series, use
direct comparison test
If your original series is < the comparison, the series converges
< converging
converges
If your original series is > the comparison, the series diverges
diverging
diverges
If you see n^a +#/n^b +# , sin (1/n), or tan (1/n), you should use
limit comparison test
lim |an/bn|
n→∞
if the lim is positive, the functions match
if you have studied all the way to this flashcard.
you must be really smart. go take a lil break. i’m proud of you. and i don’t understand most of what is on here. if you do, go take a nap. if you don’t, go take a break and come back to it later :)
