## Math 116: Study Guide - Chapter 7

1. Write the first five terms of the sequence. Two parts. Sect 1.
2. Simplify the ratio of the factorials: Two parts. Sect 1.
3. Find the sum, given in summation notation. Two parts. Sect 1.
4. Write the first five terms of the arithmetic sequence: Two parts. Sect 2.
5. Find the nth partial sum of the arithmetic sequence. Sect 2.
6. Find the sum of the arithmetic sequence, given in summation notation. Sect 2.
7. Write the first five terms of the geometric sequence. Sect 3.
8. Find the nth term of the geometric sequence. Sect 3.
9. Find the sum of the geometric sequence, given in summation notation. Two parts, one finite, one infinite. Sect 3.
10. Evaluate a combination and a permutation. Two parts. Sect 5 and sect 6.
11. Find the number of distinguishable permutations of a group of letters. Sect 6.
12. Find the probability. Two parts. Sect 7.
13. Use the Binomial Expansion Theorem to expand and simplify the expression. Sect 5.
14. Find the binomial in the difference quotient and simplify for the given function. Sect 5.
15. Find the sum using the formulas for the sums of powers of integers. Sect 4.
16. 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.