## Math 116: Study Guide - Chapter 7

- Write the first five terms of the sequence. Two parts. Look at 7.1.1 - 7.1.27
- Simplify the ratio of the factorials: Two parts. Look at 7.1.39 - 7.1.46
- Find the sum, given in summation notation. Two parts. Look at 7.1.65 - 7.1.75
- Write the first five terms of the arithmetic sequence: Two parts. Look at 7.2.19 - 7.2.31
- Find the nth partial sum of the arithmetic sequence. Look at 7.2.55 - 7.2.61
- Find the sum of the arithmetic sequence, given in summation notation. Look at 7.2.63 -
7.2.69
- Write the first five terms of the geometric sequence. Look at 7.3.21 - 7.3.25
- Find the nth term of the geometric sequence. Look at 7.3.27 - 7.3.37
- Find the sum of the geometric sequence, given in summation notation. Two parts, one finite,
one infinite. Look at 7.3.55 - 7.3.63 and 7.3.81 - 7.3.87
- Evaluate a combination and a permutation. Two parts. Look at 7.5.1 - 7.5.9 and 7.6.25 -
7.6.37
- Find the number of distinguishable permutations of a group of letters. Look at 7.6.47 - 7.6.50.
- Use the Binomial Expansion Theorem to expand and simplify the expression. Look at 7.5.17
- 7.5.31
- Find the nth term of a binomial expansion. 7.5.41 - 7.5.47
- Find a closed form for the sum. Look at problems 7.4.19 - 7.4.33
- Write the first n rows of Pascal's triangle.

### 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, n^2, n^3, n^4, n^5) - see page 558
- Formula for combination, permutation, and distinguishable permutations

- 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 70 points, the take-home portion of the test will
be worth 30 points.
- The take-home portion of the test will be due on the day of the chapter exam.