## Math 116: Study Guide - Chapter 7

- Write the first five terms of the sequence. Two parts. Sect 1.
- Simplify the ratio of the factorials: Two parts. Sect 1.
- Find the sum, given in summation notation. Two parts. Sect 1.
- Write the first five terms of the arithmetic sequence: Two parts. Sect 2.
- Find the nth partial sum of the arithmetic sequence. Sect 2.
- Find the sum of the arithmetic sequence, given in summation notation. Sect 2.
- Write the first five terms of the geometric sequence. Sect 3.
- Find the nth term of the geometric sequence. Sect 3.
- Find the sum of the geometric sequence, given in summation notation. Two parts, one finite,
one infinite. Sect 3.
- Evaluate a combination and a permutation. Two parts. Sect 5 and sect 6.
- Find the number of distinguishable permutations of a group of letters. Sect 6.
- Find the probability. Two parts. Sect 7.
- Use the Binomial Expansion Theorem to expand and simplify the expression. Sect 5.
- Find the binomial in the difference quotient and simplify for the given function. Sect 5.
- Find the sum using the formulas for the sums of powers of integers. Sect 4.
- Use mathematical induction to prove the formula for every positive integer n. Sect 4.

### Notes:

- Every problem with the exception of the distinguishable permutations (#11) is directly from the
homework.
- 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 (n, n^2, n^3, n^4, n^5) - see page 558
- Formula for combination, permutation, and distinguishable permutations
- Difference quotient.

- 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.