Algebra II: Sequences, Series and Binomial Theorem flashcards

Question 1

What is a sequence?

Accepted Answer

A function defined on the counting numbers as its domain

Question 2

What is an arithmetic sequence?

Accepted Answer

A sequence with a constant difference between consecutive terms

Question 3

What is a geometric sequence?

Accepted Answer

A sequence with a constant ratio between consecutive terms

Question 4

What is a partial sum?

Accepted Answer

The sum of finitely many terms of a sequence

Question 5

What is an annuity?

Accepted Answer

An investment made of a sequence of equal periodic deposits

Question 6

For a positive integer n, what is n!?

Accepted Answer

n(n − 1)(n − 2)…(3)(2)(1)

Question 7

What is 0!?

Accepted Answer

1

Question 8

In summation notation, what is the variable i called?

Accepted Answer

The index of summation

Question 9

General term of an arithmetic sequence: a_n = ?

Accepted Answer

a_1 + (n − 1)d

Question 10

Arithmetic series, sum of terms 1 through n: S_n = ?

Accepted Answer

(n/2)(a_1 + a_n)

Question 11

General term of a geometric sequence: a_n = ?

Accepted Answer

a_1 · r^(n−1)

Question 12

Sum of an infinite geometric series with |r| < 1: S = ?

Accepted Answer

a_1 / (1 − r)

Question 13

An infinite geometric series with |r| < 1 is said to do what?

Accepted Answer

Converge

Question 14

When does an infinite geometric series have no sum (diverge)?

Accepted Answer

When |r| ≥ 1

Question 15

How many terms are in the expansion of (a + b)^n?

Accepted Answer

n + 1

Question 16

In the expansion of (a + b)^n, what is the sum of the exponents in each term?

Accepted Answer

n

Question 17

What are the first and last terms of the expansion of (a + b)^n?

Accepted Answer

a^n and b^n

Question 18

Binomial coefficient: (n choose r) = ? (0 ≤ r ≤ n)

Accepted Answer

n! / (r!(n − r)!)

Question 19

How is the binomial coefficient (n r) read?

Accepted Answer

n choose r

Question 20

What are (n choose 0) and (n choose n)?

Accepted Answer

Both equal 1

Question 21

In the binomial theorem, the term with b^r in (a + b)^n is what?

Accepted Answer

(n choose r)·a^(n−r)·b^r

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