Unit 10 Review

Question 1

Nth Term Test

Answer 1

lim n->inf (a subn) = 0

Question 2

Nth Term lim = 0?

Answer 2

Yes- Cannot tell
No- Diverges

Question 3

P-Series p > 1?

Answer 3

Yes- Converges
No- Diverges

Question 4

Geometric Series |r| < 1

Answer 4

Yes- (ar^k)/1-r
No- Diverges

Question 5

Alternating lim = 0 AND non-increasing

Answer 5

Yes- Converges

Question 6

Comparison Test 0 <= an <= (pick) bn, bn converges

Answer 6

Yes- Converges
No- No conclusion

Question 7

Comparison Test 0 <= (pick) bn <= an, bn diverges

Answer 7

Yes– Diverges

Question 8

Limit Comparison Test lim an/(pick)bn = c, where c is positive and finite, bn converge?

Answer 8

Yes- Converges
No- Diverges

Question 9

Limit Comparison must be

Answer 9

Positive and Finite

Question 10

Integral Test an = f(n) is continuous, positive, and decreasing on [a,inf), int[a,inf] f(n) dn converge?

Answer 10

Yes- Converges
No- Diverges

Question 11

Integral Test f(n) must be

Answer 11

Continuous, Positive, and Decreasing

Question 12

Ratio Test lim|next term/an| < 1?

Answer 12

Yes- Abs. Conv.
No- Diverges
=1: No conclusion

Question 13

e^x

Answer 13

Everything NOT ALTERNATING

Question 14

sinx

Answer 14

Odd alternating (starting with x)

Question 15

cosx

Answer 15

Even Alternating (starting with 1)

Question 16

1/(1+x)

Answer 16

1-x+x^2-x^3

Question 17

Interval of Convergence

Answer 17

< 1 Converges on interval TEST ENDPOINTS
= 0 Converges on all real numbers
= inf Converges on x = c

Question 18

Lagrange Error Bound

Answer 18

Remainder <= |(MAX^(next derivative)(z(between c and x)) * (x-c)^(n + 1)) / (n + 1)!|

Question 19

Alternating Series Error Bound

Answer 19

|Sum-Partial Sum| = |Remainder| <= |Next Term|