## Math 116 Study Guide - Chapter 9

- Arithmetic Sequences / Series. Three parts (6 points)
- Find the general term of an arithmetic sequence
- Given the value of the last term, find the number of the term (find n)
- Find the sum of an arithmetic series

- Geometric Sequence / Series. Three parts (6 points)
- Find the general term of a geometric sequence
- Find a specific term of a geometric sequence
- Find the sum of an infinite geometric series.

- Evaluate the expression. Three parts (6 points)
- Factorial
- Combination
- Permutation

- Find the closed form for a summation. Write it in factored form. (3 points)
- Find a specific term in the binomial expansion. (3 points)
- Expand a binomial using the Binomial Expansion theorem. (4 points)
- Simplify the ratio of two factorials. (3 points)
- Mathematical induction. Two parts. (20 points)
- Answer the question. Five parts. (15 points)
- Find a combination
- Use the fundamental counting principle
- Find the number of distinguishable permutations
- Find a probability (look at 9.7.49 - 9.7.50)
- Find a probability (look at 9.7.29)

### Notes on Mathematical Induction problems

The two mathematical induction problems are directly from the textbook. This can not be said
about problems on the test in general. Look at problems 15 - 25 (odd and even) in section 9.4.

Realize that I will be grading the work in the Mathematical Induction problems, not the final
answer.

Here is the breakdown of points: 1 point each for writing the three *correct* steps down ("Show
n=1" is wrong). 1 point for showing true for n=1, 1 point for correctly writing what it means to
assume true for n=k, 4 points for showing true for n=k+1, and 1 point for correctly writing the
conclusion.

I will be taking off points for unbalanced or missing parentheses: "k + 1 ( k + 2)" is wrong if it
should be "( k + 1 ) ( k + 2 )".