1. ALGEBRA II HONORS/GIFTED @ CONVERGENT GEOMETRIC SERIES

2. With each bounce, a ball reaches a height equal to the height of its previous bounce. The ball is dropped from a height of 25’. A second ball, which is dropped from a height of 18’, bounces to of its previous height 1) Construct a table of values that shows the height of each ball for each bounce.

3. BounceBall 1Ball 2 1 2 3 4 5 6 7 8 9 10 2) Will ball 2 ever bounce higher than ball 1? If so, at which bounce? 3) For how many bounces do both balls stay above 10’? 4) When do the balls “stop” bouncing (theoretically speaking, of course!)?

4. 5) What happens to the sum of the series 1 + 2 + 4 + 8 + 16 + …? Given the series 6) What happens to the sum of the series as more terms are added? 7) Find each partial sum : S 5, S 10, S 50, S 100, S 500, and. Since t 1 = 5 and r =, we get

5. We can say the limit of S n converges to 10. converges to what number? CONVERGENT GEOMETRIC SERIES -1 < r < 1 8) What happens if the ratio is greater than 1? 9) What happens if the ratio is less than -1?

6. Determine if each series converges. If so, find the sum. If not, write “diverges”. 10) 15 – 4.5 + 1.35 - … 11) 2 – 3 + 4.5 - … Write as a fraction in lowest terms. 12) 0.4545… 13) 3.789789… 14) 1.4272727… 15) 0.5212121…