Name Class. Date Section. Test Form A Chapter Chapter 9 Infinite Series. 1 n 1 2 n 3n 1, n 1, 2, 3, Find the fourth term of the sequence

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1 8 Chapter 9 Ifiite Series Test Form A Chapter 9 Name Class Date Sectio. Fid the fourth term of the sequece,,,, (a) (b) 6 (c) 8 6. Determie if the followig sequece coverges or diverges: If the sequece coverges, fid its limit.,,,,.... (a) Coverges to (b) Coverges to 0 (c) Coverges to Diverges. Determie if the followig sequece coverges or diverges: If the sequece coverges, fid its limit.!!,,, 4,.... (a) Coverges to (b) Coverges to 0 (c) Coverges to Diverges 4. Fid the sum: (a) (b) (c) 6 5. Determie which of the followig series coverges. (a) (b) (c) 6. Determie which series diverges. (a) (b) 4 (c) !! Houghto Miffli Compay. All rights reserved.

2 Chapter 9 Test Bak 9 7. Determie which test ca be used to prove the divergece of the series (a) Geometric Series Test (b) p-series Test (c) Ratio Test th-term Test for Divergece. 8. Determie which test ca be used to show that the series coverges (a) Geometric Series Test (b) p-series Test (c) Ratio Test Limit Compariso Test 9. A ball is dropped from a height of 4 feet. Each time it drops h feet, it rebouds h feet. Fid the total distace traveled by the ball. (a) 7 feet (b) 44 feet (c) 0 feet 84 feet Ivestigate the series for covergece or divergece.! (a) Diverges by Ratio Test (b) Coverges by th-term Test for Divergece (c) Diverges by Root Test Coverges by Itegral Test. Ivestigate the series for covergece or divergece. l (a) Coverges by Ratio Test (c) Coverges by Root Test (b) Diverges by th-term Test for Divergece Diverges by Itegral Test Houghto Miffli Compay. All rights reserved.. Determie which of the followig series is a telescopic series. (a) (b) (c) cos. Determie if is coverget or diverget. If coverget, classify the series as absolutely coverget or coditioally coverget. (a) Diverget (b) Coditioally coverget (c) Absolutely coverget Noe of these 4. Determie which of the followig tests could be used to show that the harmoic series diverges. (a) Geometric Series Test (b) Ratio Test (c) Telescopic Series Test Itegral Test

3 0 Chapter 9 Ifiite Series 5. Fid the umber of terms ecessary to approximate the sum of the series with a error of less tha 0.00:. (a) 0 (b) 4,000,000 (c) Fid the third term of the Taylor polyomial, cetered at, for fx cos x. (a) (b) (c) 5! x x 5 5! x x 7. Fid the radius of covergece of the power series. (a) (b) (c) 0! x x 8. Determie the iterval of covergece of the series. (a), 5 (b) 5, (c) 5, 7, 9. Use the series x x x x..., to fid a power series expasio x for the fuctio fx x. (a) x x x 4... (b) x x x x4... (c) x x 4 x 6... x x x 4 x Ivestigate for covergece or divergece. (a) Coverges by Root Test (b) Diverges by Root Test (c) Coverges by Ratio Test Diverges by th-term Test for Divergece Houghto Miffli Compay. All rights reserved.

4 Chapter 9 Test Bak Test Form B Chapter 9 Name Class Date Sectio. Fid the fourth term of the sequece!,,,, (a) (b) (c) Determie if the followig sequece coverges or diverges:!,,, 4,.... If the sequece coverges, fid its limit. (a) Coverges to (b) Coverges to 0 (c) Coverges to 4 Diverges. Determie if the followig sequece coverges or diverges: If the sequece coverges, fid its limit.!,,,,.... (a) Coverges to (b) Coverges to 0 (c) Coverges to Diverges 4. Fid the sum: Houghto Miffli Compay. All rights reserved. 4 (a) (b) (c) Determie which series coverges. (a) 4 (b) (c) 5! 6. Determie which series diverges.! (a) (b) (c)! 6 5 0

5 Chapter 9 Ifiite Series 7. Determie which test ca be used to prove the divergece of the series (a) Geometric Series Test (b) p-series Test (c) Ratio Test th-term Test for Divergece. 8. A force is applied to a particle, which moves i a straight lie, i such a way that after each secod the particle moves oly oe-half the distace that it moved i the precedig secod. If the particle moved 0 cm i the first secod, how far will it move altogether? (a) 0 cm (b) 0 cm (c) 40 cm 45 cm 9. Idetify the type of series:. (a) Geometric Series (b) p-series (c) Telescopic Series Harmoic Series 0. Ivestigate for covergece or divergece. (a) Diverges by Itegral Test (b) Coverges by Alteratig Series Test (c) Diverges by th-term Test for Divergece Coverges by Ratio Test!. Determie which test would be appropriate to show that the series coverges (a) Geometric Series Test (b) p-series Test (c) Ratio Test Limit Compariso Test. Ivestigate the series for covergece or divergece (a) Coverges by th-term Test (b) Diverges by th-term Test for Divergece (c) Coverges by Root Test Coverges by Limit Compariso Test. Determie whether the series is coverget or diverget. If coverget, classify the series as absolutely coverget or coditioally coverget. (a) Diverget (b) Coditioally coverget (c) Absolutely coverget Noe of these Houghto Miffli Compay. All rights reserved.

6 Chapter 9 Test Bak 4. Determie which of the followig tests ca be used to show that coverges. (a) Root Test (b) Ratio Test (c) Geometric Series Test p-series Test 5 5. Fid the umber of terms ecessary to approximate the sum of the series with a error of less tha 0.00:. (a) 999 (b) 000 (c) Fid the third term of the Maclauri polyomial for the fuctio fx si x. (a) (b) (c)! x 5! x5 cos x! x 7. Fid the radius of covergece of the power series (a) (b) (c) 0 x. Houghto Miffli Compay. All rights reserved. x 8. Determie the iterval of covergece of the series. (a), 5 (b) 5, (c), 9. Use the series to fid a power series expasio x x x x..., for the fuctio fx l x. (a) (c) 5, 7 C x x C x x... x x Ivestigate the series for covergece or divergece. e (a) Coverges by Root Test (b) Coverges by th-term Test for Divergece (c) Coverges by Ratio Test Diverges by Geometric Series Test (b) C l x x x... C x x x x4 4...

7 4 Chapter 9 Ifiite Series Test Form C Chapter 9 Name Class Date Sectio A graphig calculator is eeded for some problems.!. Simplify:!. (a) (b) (c) a.. Let Use a graphig calculator to graph the correspodig fuctio, fx x x. The use the graph of f as a aid i determiig which of the followig statemets is true about a. (a) The sequece is ubouded. (c) The sequece is mootoic ad bouded. (b) The sequece is bouded but ot coverget. The sequece is ubouded but coverget.. Choose the series that diverges by the th-term Test for Divergece. 4 6 (a) (b) (c) 6! Determie whether the followig series is coverget or diverget. If it is coverget, fid its sum. e. e (a) Coverges to (b) Coverges to (c) Coverges to e Diverges 5. Fid the sum: e 4. (a) (b) (c) 6 0 e Houghto Miffli Compay. All rights reserved. 6. Determie which of the followig tests ca be used to show that the harmoic series diverges. (a) Geometric Series Test (b) th-term Test for Divergece (c) Telescopic Series Test Itegral Test

8 Chapter 9 Test Bak 5 7. Use the fact that 6 to fid. (a) (b) (c) Apply the Itegral Test to the series:. (a) Coverges to 4 (b) Diverges (c) Coverges The test is icoclusive 9. Determie the covergece or divergece of the series usig the Limit Compariso Test: Name the series used i the compariso.. (a) Coverges usig (c) Diverges usig (b) Coverges usig Diverges usig 0. Determie the covergece or divergece of the series by comparig it with the series ad l Use the Direct Compariso Test ad a graphig calculator to graph. the correspodig fuctios. Houghto Miffli Compay. All rights reserved. (a) Coverges by compariso with (c) Coverges by compariso with (b) Diverges by compariso with Diverges by compariso with. Fid the umber of terms ecessary to approximate the sum of the series with a error less tha 0.00: e... (a) 4 (b) 46 (c)

9 6 Chapter 9 Ifiite Series. If the series is a coditioally coverget, determie which of the followig series must diverge. a a (a) (b) (c) a a a. Ivestigate the covergece or divergece of the series: (a) Coverges by Ratio Test (c) Diverges by Ratio Test! e. (b) Coverges by Geometric Series Test Diverges by Geometric Series Test 4. Use the third Maclauri polyomial to approximate the value of e 0.. Roud your aswer to four decimal places. (a). (b).4 (c) Let f be the fuctio Fid the iterval of covergece of x fx. fx dx. (a), (b), (c),, 6. Fid a power series, cetered at, for the fuctio fx x. (a) (b) x x (c) x 4 x 4 Houghto Miffli Compay. All rights reserved.

10 Chapter 9 Test Bak 7 Test Form D Chapter 9 Name Class Date Sectio. Fid the fourth term of the sequece:,,,,..... Determie if the followig sequece coverges or diverges: If the sequece coverges, fid its limit.,,,,..... Determie if the followig sequece coverges or diverges: If the sequece coverges, fid its limit.,,,, Fid the sum: 5. Fid the sum:. 4. For each of the series i 6 through 4, determie covergece or divergece ad state the test used Houghto Miffli Compay. All rights reserved ! e 5. Fid the umber of terms ecessary to approximate the sum of the series with a error of less tha 0.00: 6. Fid the radius of covergece of the series x..

11 8 Chapter 9 Ifiite Series 7. For what values of x does the series x 4 coverge? 8. Usig the power series for si x x x x5 x7 x9 fid the power series! 5! 7! 9!..., for cos x. 9. Fid the fourth term of the Taylor Series, cetered at x, for fx l x. 0. Usig the power series e x x x x approximate (by usig four terms)!! 0.4 the value of..., e x dx. Roud your aswer to three decimal places. 0 Houghto Miffli Compay. All rights reserved.

12 Chapter 9 Test Bak 9 Test Form E Chapter 9 Name Class Date Sectio A graphig calculator is eeded for some problems. e.. Determie if the followig sequece coverges or diverges: If it coverges, fid its limit.. Cosider the sequece whose th terms is a si Use the graph of the correspodig fuctio, fx si x. as a aid i aswerig each of the followig: x, a. Determie whether a is mootoic. b. Determie whether a is bouded. c. Determie whether a coverges.. Determie whether the followig series coverges or diverges ad state the test used: Cosider the fractio a. Write the fractio as a ifiite geometric series. b. Determie the value of the first term, a, ad the commo ratio, r of the series. c. Write the series from part a usig summatio otatio.!! Use sigma otatio to write a formula for the sum of the ifiite geometric series: x x 9 x x Houghto Miffli Compay. All rights reserved. 6. Cosider the series:. a. Use the Itegral Test to show that the series coverges. b. Approximate the sum of the series usig four terms. c. Calculate the maximum error i the approximatio i part b. Roud your aswer to the earest thousadth. d. Give a upper boud for the sum of this series usig the iformatio obtaied i parts b ad c. 7. Determie the covergece or divergece of the series usig the Limit Compariso Test: Name the series used i the compariso..

13 40 Chapter 9 Ifiite Series 8. Cosider the series: l. a. Use the harmoic series as a compariso series. Name this series ad state whether it coverges or diverges. b. Compare the give series with the series amed i part a by graphig the correspodig fuctios ad applyig the Direct Compariso Test. State ad justify your coclusio. 9. Show that the series coverges by applyig the Alteratig Series Test: 0. Cosider the series:. a. Show that the series is absolutely coverget. b. Calculate the sum of the first six terms. Roud your aswer to three decimal places. c. Fid the umber of terms ecessary to approximate the sum of the series with a error less tha l.. Ivestigate the covergece or divergece of the series ad state the test used:. Let f be the fuctio fx arcta x. a. Fid the third Maclauri polyomial for f. b. Approximate the value of arcta0. usig the polyomial foud i part a... Let f be the fuctio fx x Fid the series ad the iterval of covergece forfx dx.. 4. Use the power series e x x x x x4 to fid a power series!! 4!...! for fx e x. Write the first four terms ad the geeral term of the power series. x cos 5. Use the trigoometric idetity cos ad the power series cos x to fid a power series for the fuctio fx cos x. x! Houghto Miffli Compay. All rights reserved.