MATH 142 - Dillon

Series Rules

100

What are the terms of convergence for a series in the form 1/(k ^ p)?

when p>1, the series will converge

200

What are the three guidelines you MUST check before doing the Integral test?

1. positive

2. continuous

3. decreasing

300

When are the Ratio/Root Tests inconclusive?

When L or rho is equal to 1. Another test must be done when this happens. 

400

What are the steps we must follow to determine if a series converges by the Alternating Series Test?

1. Alternating

2. The series of u_n or a_k must be decreasing

3. lim (n->infinity) u_n or a_{k = 0}

500

What are the rules of convergence/divergence for the Direct Comparison Test?

*0<=a<=b

If the series of b_n converges, then the series of a_n also converges. 

If the series of a_n diverges, then the series of b_n also diverges. 

Need to Know

100

What series test ONLY tests for divergence?

The Nth Term Divergence Test

200

Which formula is used for convergence of the Geometric Series Test?

a/(1-r) where a is the first term in the series

300

Which two series/series tests can solve for the convergence of a series?

1. Geometric Series Test

2. Telescoping Series

400

What is the difference between a sequence and a series?

A sequence is a list of numbers while a series is a sum of the list of those numbers

500

Explain how a series can converge absolutely. 

The original series must converge by the Alternating Series Test, plus, the absolute value of that series must converge. This can also be tested by the generalized ratio or root test.

Practice Test Questions

100

Question 3

Because |r|<1 for both series, the series converges to 73/300 by the geometric series test

200

Question 2

Because the limit of the series does not equal zero, the series diverges by the Nth term divergence test.

300

Question 4

Because rho > 1, the series diverges by the Root Test

400

Question 1

Because rho<1, the series converges absolutely by the Ratio Test

500

Question 7

The series is a telescoping series and converges to 1

Grab Bag

100

Write a formula for the general term of the following sequence:

1,1,2,6,24,120,720,....

n!

200

What does 2.3(repeating) converge to?

7/3

300

Does the series of (pi/n ^ e) converge or diverge?

Converges by the p-series test

400

Does the series of ln(n)/(n^3) converge or diverge? On the interval from (6, infinity)

Converges by either limit comparison test (comparing to 1/(n^2)) or by the q-log series test.

500

What is special about the Alternating harmonic series and explain?

It is conditionally convergent, meaning it converges by the Alternating Series Test but diverges when the absolute value of the series is taken. 

Hocus Pocus

100

What town does the movie take place in?

Salem 

200

What is the cat's name who helps the children throughout the movie?

Thackery Binx (Binx will be accepted)

300

What iconic halloween song does Winifred sing at the halloween party?

"I put a spell on you"

400

What was so special about Max that him lighting the candle brought the Sanderson sisters back?

He was a virgin

500

Name one actress who plays one of the Sanderson Sisters. 

1. Bette Midler

2. Sarah Jessica Parker

3. Kathy Najimy