AP Calculus: Sequences and Series flashcards

Question 1

What is an ordered list of numbers a₁, a₂, a₃, … called?

Accepted Answer

A sequence

Question 2

What is the number aₙ in a sequence {aₙ} called?

Accepted Answer

The nth term of the sequence

Question 3

What is the subscript n that labels the terms of a sequence called?

Accepted Answer

The index

Question 4

What kind of sequence has the same difference between every pair of consecutive terms?

Accepted Answer

An arithmetic sequence

Question 5

What kind of sequence has the same ratio aₙ₊₁/aₙ for every positive integer n?

Accepted Answer

A geometric sequence

Question 6

A sequence {aₙ} has a constant M with aₙ ≤ M for all positive integers n. What is it called?

Accepted Answer

Bounded above

Question 7

A sequence {aₙ} has a constant M with M ≤ aₙ for all positive integers n. What is it called?

Accepted Answer

Bounded below

Question 8

What is an increasing or decreasing sequence called?

Accepted Answer

A monotone sequence

Question 9

What is a sequence called when aₙ gets arbitrarily close to some real number L for large enough n?

Accepted Answer

A convergent sequence

Question 10

What is the real number L to which a convergent sequence converges called?

Accepted Answer

The limit of the sequence

Question 11

What is a sequence that is not convergent called?

Accepted Answer

A divergent sequence

Question 12

What do you call a relationship that defines a term aₙ using earlier terms of the sequence?

Accepted Answer

A recurrence relation

Question 13

What is an expression of the form a₁ + a₂ + a₃ + ⋯, written Σₙ₌₁^∞ aₙ, called?

Accepted Answer

An infinite series

Question 14

What is the finite sum Sₖ = a₁ + a₂ + ⋯ + aₖ of an infinite series called?

Accepted Answer

The kth partial sum

Question 15

A series converges if which sequence converges?

Accepted Answer

Its sequence of partial sums

Question 16

A series diverges if which sequence diverges?

Accepted Answer

Its sequence of partial sums

Question 17

What is a series of the form Σₙ₌₁^∞ a·rⁿ⁻¹ = a + ar + ar² + ⋯ called?

Accepted Answer

A geometric series

Question 18

What is the series Σₙ₌₁^∞ 1/n = 1 + 1/2 + 1/3 + ⋯ called?

Accepted Answer

The harmonic series

Question 19

What is a series of the form Σₙ₌₁^∞ 1/nᵖ called?

Accepted Answer

A p-series

Question 20

What is a series called when most of the terms cancel in each partial sum?

Accepted Answer

A telescoping series

Question 21

What is a series of the form Σ(−1)ⁿ⁺¹bₙ or Σ(−1)ⁿbₙ, with bₙ ≥ 0, called?

Accepted Answer

An alternating series

Question 22

If Σ|aₙ| converges, in what way is the series Σaₙ said to converge?

Accepted Answer

Absolutely (absolute convergence)

Question 23

If Σaₙ converges but Σ|aₙ| diverges, in what way does Σaₙ converge?

Accepted Answer

Conditionally (conditional convergence)

Question 24

Which test says Σaₙ diverges if the limit of aₙ as n → ∞ is not 0?

Accepted Answer

The divergence test

Question 25

Which test says an alternating series converges if bₙ₊₁ ≤ bₙ for all n ≥ 1 and bₙ → 0?

Accepted Answer

The alternating series test

Question 26

Which test says that if 0 ≤ aₙ ≤ bₙ for all n ≥ N and Σbₙ converges, then Σaₙ converges?

Accepted Answer

The comparison test

Question 27

In the root test, with ρ = lim of the nth root of |aₙ|, what does ρ = 1 tell you?

Accepted Answer

The test is inconclusive

AP Calculus: Sequences and Series flashcards

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