Studied by 9 people

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Hint

1

Which test should you always start with?

nth term test

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2

lim n→∞ an=0

nth term test is inconclusive

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3

lim n→∞ an doesn’t =0

inconclusive, use another test

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4

1/n^p

p >1

series converges by p-series

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5

1/n^p

p≤ 1

series diverges by p-series

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6

∑a(r)ⁿ

|r|<1

series converges by geometric series

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7

∑a(r)ⁿ

|r|≥1

series diverges by geometric series

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8

which test should you use when you see ∑(an)ⁿ

root test

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9

lim n→∞. ⁿ√|an| < 1

series converges by root test

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10

lim n→∞. ⁿ√|an| > 1

series diverges by root test

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11

which test should use you when you see factorials and exponentials

ratio test

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12

lim n→∞ |an+1/an| < 1

series converges by ratio test

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13

lim n→∞ |an+1/an| >1

series diverges by ratio test

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14

when you see (-1)ⁿ

use alternating series test, if terms are dec in abs value towards 0

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15

lim n→∞ |an| = 0

series converges by alt srs test

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16

lim n→∞ |an| doesn’t = 0

doesn’t converge by alt srs, use nth term test to prove divergence

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17

If you see a series where there would be a u-sub, use

integral test if the series is positive, cont, and dec

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18

lim b→∞ ∫ from b to ∞. = #

series converges by integral test

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19

lim b→∞ ∫ from b to ∞. = ∞

series diverges by integral test

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20

If a series looks < or > a similar series, use

direct comparison test

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21

If your original series is < the comparison, the series converges

< converging

converges

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22

If your original series is > the comparison, the series diverges

diverging

diverges

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23

If you see n^a +#/n^b +# , sin (1/n), or tan (1/n), you should use

limit comparison test

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24

lim |an/bn|

n→∞

if the lim is positive, the functions match

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25

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 :)

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