Math 115 Spring 2014
Written Homework 4
Due Friday, February 28
Instructions: Write complete solutions on separate paper (not spiral bound). If
multiple pieces of paper are used, THEY MUST BE STAPLED with your name
and lecture written on each page. Please review the Course Information document for more complete instructions.
1. If 4a1 , 4a2 , 4a3 , ..., 4an is a geometric sequence, what can you determine about the sequence
a1 , a2 , a3 , ..., an ?
2. Write
7
X
|2π − k| as an expanded sum and compute the sum.
k=2
3. Write each of the following using summation notation.
(a) (a1 )3 b1 + (a2 )4 b2 + (a3 )5 b3 + ... + (a10 )12 b10
(b) The sum of all three digit positive odd integers.
2 2
2
(c) 6 − 2 + − + ... +
3 9
243
4. If
4
X
2
(a b − ab) =
b=2
5
X
(ac + 6), determine a.
c=3
5. What is the sum of the series
n
X
(−2)k , if n is odd? if n is even?
k=1
6. Compute the sum
36
X
[2 + 3(n − 1)].
n=20
7. Evaluate each geometric series.
1
(a) The first and last terms of summation are 8 and 512
, respectively and the common ratio
between each term is 41 .
(b) The sum of −3 + 6 − 12 + 24 − ... where the associated sequence has 21 terms.
8. How many terms of the sequence generated by the function an := 4(3)n−1 must be added to
give a sum of 1456?
9.
(a) Use a series formula we discussed to find the sum of the first 200 even, positive integers.
(b) Use a series formula we discussed to find the sum of all positive integers less than 200 that
are multiples of 6.
10. Your roommates want you to help clean the kitchen in you apartment on a regular basis.
You get them to agree to pay you $0.01 the first day, $0.02 the second day, $0.04 the third,
$0.08 the fourth, and so on. What will they be paying you on the 30th day? At the end of 30
days, how much will they have paid you total?