Calc III Test 1

Question 1

Nth term Test

Answer 1

If the terms go to 0 the series could either converge or diverge. If terms don’t go to 0 the series definitely diverges.

Question 2

Geometric

Answer 2

Fixed Number Identity
A and R Rules
r<1
a/1-r

Question 3

Telescoping

Answer 3

1 term minus a similar term (end up cancelling out)

Question 4

Integral Test

Answer 4

Change n to “x”- Can we Integrate?

Question 5

Comparison Test

Answer 5

Guess right
Convergence- a ≤ and b converges
Divergence b≤a and b diverges

Question 6

Limit Comparison Test

Answer 6

lim n–>inf aN/bN= C>0 for large An/Bn=C –> An= C*bN

Question 7

P Series Rules

Answer 7

1/n^p
p ≤1- Diverges
p>1- Converges