Math 116: Study Guide - Chapter 7

1. Write the first five terms of the sequence. Two parts. Look at 7.1.1-22, 29-34
2. Find the most apparent pattern for the general term of the sequence. Two parts. Look at problems 7.1.51-64
3. Simplify the ratio of the factorials: Two parts. Look at 7.1.69-78
4. Find the sum, given in summation notation. Two parts. Look at 7.1.79-90
5. Write the first five terms of the arithmetic sequence. Look at 7.2.17-20
6. Find the nth term of the arithmetic sequence. Look at problems 7.2.25-28, 41-44 although these aren't exactly like the problem on the test. After finding the general term for the sequence, you need to plug in the number of the term asked for.
7. Find the nth partial sum of the arithmetic sequence. Look at 7.2.59-64
8. Use the formula for the nth partial sum of an arithmetic series to find the sum of the arithmetic sequence, given in summation notation. Look at 7.2.65-78
9. Write the first five terms of the geometric sequence. Look at 7.3.21-26
10. Find the nth term of the geometric sequence. Look at 7.3.33-36
11. Use the formula for the nth partial sum of a geometric series to find the sum of the geometric sequence, given in summation notation. Look at problems 7.3.55-64.
12. Find the sum of the infinite geometric series. Look at problems 7.3.69-80
13. Evaluate a combination and a permutation. Two parts. Look at 7.5.13-18 and 7.6.33-38
14. Find the number of distinguishable permutations of a group of letters. Look at 7.6.43-46
15. Use the Binomial Expansion Theorem to expand and simplify the expression. Look at 7.5.23-40
16. Find the nth term of a binomial expansion. 7.5.49-56
17. Find a closed form for the sum. Look at the take home test. Know the formulas for the sums of the powers of integers from page 530.

Notes:

• You may bring in a set of note cards with the following formulae:
  • Arithmetic Sequences / Series: Common Difference, General Term, Sum of the first n terms (two formulas)
  • Geometric Sequences / Series: Common Ratio, General Term, Sum of the first n terms, Sum of an infinite series
  • Sum of the powers of the integers (1, n, n², n³, n⁴, n⁵) - see page 530
  • Formula for combination, permutation, and distinguishable permutations
• You may NOT put examples on the note cards
• It would be wise to put each section of notes on a separate card, rather than trying to cram too much onto one card. Write large enough it's legible, and check for accuracy.
• The Binomial Expansion Theorem may NOT be on a note card.
• Because of the time it will take to work a mathematical induction problem, the mathematical induction problems have been moved to a take home test.
• The in-class portion of the test will be worth 75 points, the take-home portion of the test will be worth 25 points.
• The take-home portion of the test will be due on the day of the chapter exam.