WebAssign Lesson 6-1b Geometric Series (Homework)

Transcription

1 WebAssig Lesso 6-b Geometric Series (Homework) Curret Score : / 49 Due : Wedesday, July :0 AM MDT Jaimos Skriletz Math 75, sectio 3, Summer Istructor: Jaimos Skriletz. /2 poitsrogac alcet State whether or ot the followig series are geometric. (a) This is a geometric series. This is ot a geometric series. (b) 5 3 This is a geometric series. This is ot a geometric series. (c) This is a geometric series. This is ot a geometric series. (d) π 5 This is a geometric series. This is ot a geometric series.

2 2. / poits Which of the followig series are geometric. Select all that apply. 7! e /3 poits Fid the exact values of the followig geometric series. If the quatity diverges, eter DIVERGES

3 4. /3 poits Fid the exact values of the followig geometric series. If the quatity diverges, eter DIVERGES e 5. /3 poits Cosider the geometric series that starts at a o- zero value 5 3 You ca fid the exact value of this series by rewritig it i a stadard form for a geometric series.. Method I: Add/Subtract the missig terms to rewrite the geometric series as Method II: Factor (multiply/divide) ad rewrite the series as Note: Startig at 3 but usig a power of - 3 is the same as startig at zero with a power of. 3. Use either (or check both) of the above methods to fid the exact value of this series? 3 5

4 6. /3 poits Fid the exact values of the followig geometric series usig either of the methods i the above problem. If the quatity diverges, eter DIVERGES π /2 poitsrogac alcet /2 poitsrogac alcet

5 9. /2 poitsrogac alcet e 5 0. /2 poitsrogac alcet π 3e. /2 poitsrogac alcet Additioal Materials CalcClip

6 2. /2 poitsrogac alcet ( 3) /2 poitsrogac alcet Use the formula for the sum of a geometric series to fid the sum /2 poitsrogac alcet ( 2) 5 8 0

7 5. /2 poits A 2 foot by 2 foot square is cut ito a ifiite umber of triagles (as show). The first has a width of feet, the secod a width of feet, the third a width of feet, ad so o What is the total area of the triagles? (Hit: Write the area as a ifiite series.) Area

8 6. /2 poitsrogac alcet A ball dropped from a height of h 20 ft begis to bouce. Each time it strikes the groud, it 2 2 returs to of its previous height a 5 5. What is the total distace traveled by the ball if it bouces ifiitely may times? ft 7. /3 poits Cosider the repeatig decimal sequece Write this umber as a fractio of itegers by. Express the umber as a geometric series. Hit: Express this umber as a ratio of two itegers

9 8. /2 poits Cosider the repeatig decimal sequece Viewig Saved Work Revert to Last Respose Write this umber as a fractio of itegers by. Let s Set up the equatio 00s s 3. Solve the above equatio for s, aswer as a ratio of two itegers. s /3 poits Write the followig repeatig decimal sequeces as a fractio of whole umbers

10 20. /3 poits The geometric series formula writes the followig fuctio as a series x. Take the derivative of each side of the above equatio. (Hit: The derivative of a coverget series is the sum of the derivative of the terms like a fiite sum.) x d dx x d x dx 2. Use the above to fid the exact value of the sum 3 2. /3 poits The geometric series formula writes the followig fuctio as a series x x. Take the itegral of each side of the above equatio. (Assume the costat of itegratio is 0.) x x 2. Use the above to fid the exact value of the sum (/4) + +