Ch 3. Sequences, Sums & Induction

What is permutations

A permutation is an arrangement, or ordering, of a set of objects. ex. The total number of permutations of the six horses is 6 x 5 x 4 x 3 x 2 x 1 = 720.

What's the difference between a sequence and a series?

A sequence is an ordered list of numbers, and a series is the sum of a sequence's terms.

What is the first step of mathematical induction?

Prove the first case, usually n = 1, is true.

What is the first step in mathematical induction?

Prove the statement is true for the first element in the set.

What do you need to do to prove the second step of mathematical induction?

Show that both sides of the statement equal each other.

What do you have to assume in mathematical induction?

The case n = k is true.

Two steps of mathematical induction

The first is to prove that our first case is true. The second is to prove that if any other case is true, then the following case is also true.

Arithmetic formula

n/2 (a1+a2)

To calculate permutations, we use the equation and also what to solve

nPr and to solve nPr = n! / (n - r)!

A discrete random variable is a variable that represents

numbers found by counting. For example: number of marbles in a jar, number of students present or number of heads when tossing two coins.

Do sequences have order?

yes

Perform the first step of mathematical induction for the mathematical statement n + 1 > n.

2 > 1 --> 1+1 > 1 --> 2>1

Infinite sequence symbol

'.....' at the end

Fixed circle formula

(n-1)!

Free circle formula

(n-1)!/2

What is fundamental counting principle

This principle states that if there are p possibilities for one event and q possibilities for a second event, then the number of possibilities for both events is p x q

what circle is intended unless otherwise specified

fixed (n-1)

What symbol is term count of a sequence

a

Arithmetic sequence

a sequence in which each term is found by adding the same number to the previous term

geometric sequence

a sequence in which each term is found by multiplying the previous term by the same number

What is mathematical induction

a way of proving a mathematical statement by saying that if the first case is true, then all other cases are true, too.

Geometric series formula

a(1-r^n)/1-r

If a geometric series begins with the following term a1, what would the next term be?

a1 * r

formula for infitnite value of a serie

a1 / (1-r)

What is the rule for the nth term of the sequence with a7 = 53 and a13 = 101?

an = 8n - 3

Recursive Sequence

any sequence that depends on the values of the previous

Combinatorics is a branch of mathematics that has to do with

counting techniques

2 ways of calculating pos outcomes

dependent on the type of event and the structure of event