Chapter 11 Review (Test 1) Flashcards Preview

AP Calc BC > Chapter 11 Review (Test 1) > Flashcards

Flashcards in Chapter 11 Review (Test 1) Deck (16):
1

Sequence

bracket a sub n bracket from n = 1 to infinity.
A sequence is a listing of values of a sub n as n goes from 1 to infinity.

2

Arithmetic sequence

Each term is the sum of the previous term and a constant (called the common difference).
a sub n = a sub 1 plus (n-1)*d

3

Geometric Sequence

each term is the product of the previous term and a constant (coalled the common ratio).
a sub n = a sub 1 * r to the n-1 power.

4

limits of sequences

the sequence of {a sub n} converges to L if limit as n approaches infinity of a sub n = L.
the sequence of {a sub n} diverges if limit of a sub n diverges. (equals infinity)
*remember to test for even and odd terms when dealing with sequences with (-1) to the n or n+1 power

5

A sequence converges to L if and only if:

the even numbered terms converge to L and the odd numbered terms converge to L.

6

Recursive sequences

a sequence in which you are given an initial term and a formula to find the subsequent terms.

7

Limits of Recursive Sequences

a sequence defined recursively will converge if:
limit as n approaches infinity of a sub n+1 = limit as n approaches infinity of a sub n = L.
Steps:
1. Set limit as n approaches infinity of a sub n equal to L.
2. Set limit as n approaches infinity of a sub n + 1 (with L substituted in) equal to L.

8

Series

Adding terms

9

Infinite series

a series with an infinite number of terms.

10

Convergence of an infinite series

If an infinite series converges to L, then the sum equals L. An infinite series converges if the sequence of partial sums converge.

11

Convergence of an Infinite Geometric Series

An infinite geometric series converges if absolute value of r < 1 AND it converges TO a sub 1 divided by 1 minus r/

12

Divergence of an Infinite Geometric Series

An infinite geometric series diverges if the absolute value of r is greater than or equal to 1.

13

Telescoping Series

Ex: 1 divided by 1*2 plus 1 divided by 2*3 plus 1 divided by 3*4 and so on. (not geometric). Turn into partial fractions and then plug k back in and cancel everything out.

14

Harmonic Series

ex: sigma from k=1 to infinity of 1 divided by k. Diverges.

15

Divergence Test

Let a sub k be the general term of sigma a sub k.
If limit as k approaches infinity of a sub k does not equal 0, then sigma a sub k diverges.
If limit as k approaches infinity of a sub k = 0, then sigma of a sub k may converge or diverge (test is inconclusive).

16

Properties of Series

sigma of U sub k plus or minus v sub k = sigma u sub k plus sigma of v sub k.
sigma of c times u sub k equals c times sigma u sub k.