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JEOPARDY. ID, Please!. Compared to What?!. The 3 R's. I'm All Shook Up. Back and Forth. $200. $200. $200. $200. $200. $400. $400. $400. $400. $400. $600. $600. $600. $600. $600. $800. $800. $800. $800. $800. $1000. $1000. $1000. $1000. $1000.
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ID, Please! Compared to What?! The 3 R's I'm All Shook Up... Back and Forth $200 $200 $200 $200 $200 $400 $400 $400 $400 $400 $600 $600 $600 $600 $600 $800 $800 $800 $800 $800 $1000 $1000 $1000 $1000 $1000
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ANSWER 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
DONE ID, Please! - $200 A Convergent Geometric Series since r < 1.
DONE ID, Please! - $400 A Divergent Geometric Series since r > 1.
DONE ID, Please! - $600 A Divergent p – Series since p < 1.
DONE ID, Please! - $800 The limit of this series equals 1, therefore by the nth term test, the series DIVERGES.
DONE ID, Please! - $1000 This series can be written as which is just a convergent p – series, since p > 1
DONE Compared to What?! - $200 Using the Direct Comparison Test to the convergent series Therefore, this series converges also.
DONE Compared to What?! - $400 Use the Limit Comparison Test with Since converges, so does the original series.
DONE Compared to What?! - $600 Using the Direct Comparison Test to the convergent p – series Therefore, this series converges also.
DONE Compared to What?! - $800 Using the Direct Comparison Test to the convergent geometric series Therefore, this series converges also.
DONE Compared to What?! - $1000 Using the Direct Comparison Test, we first try So try using the Direct Comparison Test with something in between … say BUT this gives us a series that is less than a divergent series … Not helpful Next, try using the Direct Comparison Test with Therefore, since the series is less than a convergent series, the original series is CONVERGENT ALSO! BUT this gives us a series that is more than a convergent series … Not helpful
DONE The 3 R's - $200 By the Root Test, this series converges.
DONE The 3 R's - $400 By the Ratio Test, this series diverges.
DONE The 3 R's - $600 By the Integral Test, this series converges because the integral converges. NOTE: you could have used the geometric series test since
DONE The 3 R's - $800 By the Integral Test, this series diverges because the integral diverges.
DONE The 3 R's - $1000 By the Ratio Test, this series converges.
DONE I'm All Shook Up... - $200 By the Telescoping Series Test, this series converges.
DONE I'm All Shook Up... - $400 A convergent p – series, since p > 1
DONE I'm All Shook Up... - $600 Using the Limit Comparison Test to the divergent p – series Therefore, since the p – series diverges, so does the original series.
DONE I'm All Shook Up... - $800 By the Ratio Test, this series diverges.
DONE I'm All Shook Up... - $1000 By the nth term Test, since this series diverges
DONE Back and Forth - $200 Alternating Series Test (condition 1): (condition 2): Since both conditions of the alternating series are met, the series converges.
