Back and Forth I'm All Shook Up... The 3 R'sCompared to What?! ID, Please! $1000 $800 $600 $400 $200.

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Presentation transcript:

Back and Forth I'm All Shook Up... The 3 R'sCompared to What?! ID, Please! $1000 $800 $600 $400 $200

Click here to go back to the main board You have selected an area of the board not in play.

ID, Please! - $200 ANSWER

ID, Please! - $400 ANSWER

ID, Please! - $600 ANSWER

ID, Please! - $800 ANSWER

ID, Please! - $1000 ANSWER

Compared to What?! - $200 ANSWER

Compared to What?! - $400 ANSWER

Compared to What?! - $600 ANSWER

Compared to What?! - $800 ANSWER

Compared to What?! - $1000 ANSWER

The 3 R's - $200 ANSWER

The 3 R's - $400 ANSWER

The 3 R's - $600 ANSWER

The 3 R's - $800 ANSWER

The 3 R's - $1000 ANSWER

I'm All Shook Up... - $200 ANSWER

I'm All Shook Up... - $400 ANSWER

I'm All Shook Up... - $600 ANSWER

I'm All Shook Up... - $800 ANSWER

I'm All Shook Up... - $1000 ANSWER

Back and Forth - $200 ANSWER

Back and Forth - $400 ANSWER

Back and Forth - $600 ANSWER

Back and Forth - $800 ANSWER

Back and Forth - $1000 ANSWER

****Answers****

ID, Please! - $200 DONE A Convergent Geometric Series since r < 1.

ID, Please! - $400 DONE A Divergent Geometric Series since r > 1.

ID, Please! - $600 DONE A Divergent p – Series since p < 1.

ID, Please! - $800 DONE The limit of this series equals 1, therefore by the nth term test, the series DIVERGES.

ID, Please! - $1000 DONE This series can be written as which is just a convergent p – series, since p > 1

Compared to What?! - $200 DONE Using the Direct Comparison Test to the convergent series Therefore, this series converges also.

Compared to What?! - $400 DONE Use the Limit Comparison Test with Since converges, so does the original series.

Compared to What?! - $600 DONE Using the Direct Comparison Test to the convergent p – series Therefore, this series converges also.

Compared to What?! - $800 DONE Using the Direct Comparison Test to the convergent geometric series Therefore, this series converges also.

Compared to What?! - $1000 DONE Using the Direct Comparison Test, we first try BUT this gives us a series that is less than a divergent series … Not helpful Next, try using the Direct Comparison Test with BUT this gives us a series that is more than a convergent series … Not helpful So try using the Direct Comparison Test with something in between … say Therefore, since the series is less than a convergent series, the original series is CONVERGENT ALSO!

The 3 R's - $200 DONE By the Root Test, this series converges.

The 3 R's - $400 DONE By the Ratio Test, this series diverges.

The 3 R's - $600 DONE this series converges because the integral converges. By the Integral Test, NOTE: you could have used the geometric series test since

The 3 R's - $800 DONE this series diverges because the integral diverges. By the Integral Test,

The 3 R's - $1000 DONE By the Ratio Test, this series converges.

I'm All Shook Up... - $200 DONE By the Telescoping Series Test, this series converges.

I'm All Shook Up... - $400 DONE A convergent p – series, since p > 1

I'm All Shook Up... - $600 DONE Using the Limit Comparison Test to the divergent p – series Therefore, since the p – series diverges, so does the original series.

I'm All Shook Up... - $800 DONE By the Ratio Test, this series diverges.

I'm All Shook Up... - $1000 DONE By the nth term Test, since this series diverges

Back and Forth - $200 DONE Alternating Series Test (condition 1): (condition 2): Since both conditions of the alternating series are met, the series converges.

Back and Forth - $400 DONE Alternating Series Test (condition 1): Since the first condition of the alternating series test fails, then what we just did is the equivalent of the nth term test. Therefore, this series diverges.

Back and Forth - $600 DONE Alternating Series Test (condition 1): (condition 2): To show it is decreasing, find the 1 st derivative The 1 st derivate is 0 for x = 1, but negative everywhere else. Therefore, both conditions are met and the series converges.

Back and Forth - $800 DONE Alternating Series Test (condition 1): Since the first condition of the alternating series test fails, then what we just did is the equivalent of the nth term test. Therefore, this series diverges.

Back and Forth - $1000 DONE First, recognize this as an Alternating Series … since (condition 1): (condition 2): Since both conditions of the alternating series are met, the series converges.

CONTINUE

Directions for Changing the Game To change the questions and answers, just type over the problems…Use the “replace” feature to change the categories easily The daily doubles were originally set to category #1 for $800 and category #5 for $400 To change the daily doubles you must –1. Change the hyperlink for the links on the main board to go to the appropriate question, therefore bypassing the daily double slide … (right click on category #1 for $800 and chose hyperlink, then edit hyperlink) –2. There is a rectangle drawn around each slide that is used to link the slide question with the answer (or answer back to the main board). To change this link, position your cursor at the edge of the slide to select the rectangle and edit the hyperlink by right clicking the rectangle. You need to edit the hyperlink on each Daily Double slide.