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1 Convergent, 0 Divergent Convergent 150 Convergent 28.78787878 2 2091.946 3 |r| < 1 4 59th term 0.958 5 Example a n = 3n 3 +3n 2n 6 28 terms 7 Example 5, 3.75, 2.8125, 2.109375,... 8 2097151 9 a 1 = 17 a n = a n-1 + 8 n > 1 10 22.5 miles 11 -50300 44408920906.885
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Convergent 150 Convergent 28.78787878
2 2091.946
3 |r| < 1
4 59th term 0.958
5 Example an = 3n3 +3n
2n
6 28 terms
7 Example 5, 3.75, 2.8125, 2.109375,...
8 2097151
9 a1 = 17
an = an-1 + 8 n > 1
10 22.5 miles
11 -50300 44408920906.885
12 46.2222221863 46.22222222222222
13 Divergent, because the ratio is 3.33333 which is larger than one, so the sequence grows to infinity and the series will also grow to infinity
14 a. 88200
b. 495
c. 1860480
d. 190
15 x5 - 15x4 + 90x3 - 270x2 + 405x - 243
16 -16,796,160
17 8 + -36b2 + 54b4 + -27b6
18 0.322
19. a. 0.493
b. 0.9999078
Chapter 8
write as a recursive formula
Find the sum of the following series
5 + 8 + 11 + … + 1808 + 1811
Name the Movie and Character(s)
An infinite geometric sequence has a constant ratio of 1/5 and a sum of 218. Find its first term.
A classroom has 15 females and 11 males. How many groups of 5 with exactly 3 females are possible?
Find the probability of rolling 10 six sided dice and getting at least 8 fives.
The sum of first 68 terms of an arithmetic series is 10591. If the first term is 5, what is the constant difference?
Write an explicit expression that gets closer and closer to 12/19 as you have more and more terms.
In a class of 12 students a teacher needs to pick 3 students to go shopping for the end of the year party. How many ways can this be done?
In Pascal's Triangle, what is the highest row number with a sum less than 200,000?
Name the Movie and Character(s)
Expand and simplify without a calculator.
(2x5 + y3)4
an = an-1 - 3 n>1
2. 1
3.
4. 547524
5. 179.99898
6.
7. 174.4
8. 25025
9.
10 330
11 2029809375
12
13 .00019449
14 4.5
15
16 Example bn = 3x2 + 12x5
19x5
17 Divergent
18
19 220
20 17th row
21
22 16x20 + 32x15y3 + 24x10y6 + 8x5y9 + y12
23 there are repeated trials
trails are independent
fixed number of trials
probabilities are the same for each trail
2 outcomes
