Calc 2 Tests

Question 1

Geometric Series Convergence

Answer 1

r < 1

Question 2

Geometric Series Divergence

Answer 2

r > or equal to 1

Question 3

Formula for finding the convergence with the G.S.T

Answer 3

a/(1-r)

Question 4

Divergence Test Convergence

Answer 4

Does not apply! Only tells you if you are divergent

Question 5

Divergence Test Divergence

Answer 5

the limit as k goes to infinity of ak is NOT zero. Meaning that if you get a real number then the test diverges.

Question 6

Can the divergence test be used to prove convergence?

Answer 6

NO, only divergence through the limit of a non-zero positive number

Question 7

What do you need the f(x) to be for the integral test?

Answer 7

f is continuous, positive, decreasing

Question 8

Integral test for convergence

Answer 8

If you take the integral of the function with one of the bounds as infinity and its less than infinity

Question 9

Integral Test for Divergence

Answer 9

the integral does not exist

Question 10

Can you find the convergence/divergence value with the integral test?

Answer 10

No, the value of the integral is not the value of the series

Question 11

P-series condition for convergence

Answer 11

p >1

Question 12

p-series condition for divergence

Answer 12

p < or equal to 1

Question 13

What is the p-series test useful for?

Answer 13

comparison tests!

Question 14

ratio test condition for convergence

Answer 14

the ratio thingy is less than 1. the limit as k –> ∞ of (ak+1)/ak < 1

Question 15

ratio test condition for divergence

Answer 15

limit as k–> ∞ of (ak+1)/ak > 1

Question 16

What if you get 1 for the limit of the ratio test?

Answer 16

the test is inconclusive

Question 17

root test condition for convergence

Answer 17

limit as k –> ∞ of the kth root of ak < 1

Question 18

root test condition for divergence

Answer 18

limit k –> ∞ of the kth root of ak > 1

Question 19

what if you get 1 for the limit of the root test?

Answer 19

its inconclusive

Question 20

condition for the comparison test for convergence

Answer 20

0 < ak < or equal to bk and the sum of bk converges

Question 21

condition for the comparison test for divergence

Answer 21

0 < bk< or equal to ak and the sum of bk diverges

Question 22

what is unique about the comparison and the limit comparison test?

Answer 22

the sum of ak is given, you supple bk

Question 23

condition for the limit comparison test for convergence

Answer 23

0 < or equal to the limit of ak/bk < ∞ and the sum of bk converges

Question 24

condition for the limit comparison for divergence

Answer 24

the limit of ak/bk > 0 and the sum of bk diverges

Question 25

condition for the alternating series test for convergence

Answer 25

the limit as k–> ∞ = 0

Question 26

condition for the alternating series test for divergence

Answer 26

the limit as k –> ∞ ak DOESNT EQUAL 0