Calculus 3 - Sequences and Series

alternating

-1, 1/2, -1/2, 1/4, -1/5, ... is an example of an ___ sequence

Telescoping Series Test

A series whose partial sums eventually only have a fixed number of terms after cancellation

logarithms, trig, or exponential. It also doesn't work when n isn't the base. (i.e. a^n doesn't work for Dom Terms)

Dominant Terms does not work with...

3 4 5 6 7 3 7 12 18 25

Find the first 5 terms... infinity ^E (n = 1) = ? + ? + ? + ? + ? S1 = ? S2 = ? S3 = ? S4 = ? S5 = ?

0

If the denominator is larger, the answer will be...

the coefficients

If the exponents in the numerator and denominator tie, the answer will be...

infinity

If the numerator is larger, the answer will be...

Squeeze Theorem

If two functions squeeze together at a particular point, then any function trapped between them will get squeezed to that same point. The Squeeze Theorem deals with limit values, rather than function values. The Squeeze Theorem is sometimes called the Sandwich Theorem or the Pinch Theorem.

Factorial

The product of all whole numbers except zero that are less than or equal to a number

partial sum of an arithmetic series

The sum of a limited number of terms of an infinite arithmetic sequence.

smaller larger

When canceling factorials, you first decide whether the numerator or denominator is larger, then you leave the ___ half alone and break up the ___ half.

dominant

When solving for the limit of a sequence, you can use ___ terms

recursively defined sequence

a sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms

sequence

an ordered list of numbers

geometric sequence

an=a1(r)^n-1 a sequence in which each term is found by multiplying the previous term by the same number

arithmetic sequence

an=a1+(n-1)d a sequence in which each term is found by adding the same number to the previous term

an=a1+(n-1)d

arithmetic sequence formula

an=a1(r)^n-1

geometric sequence formula

an+1

next term

an-1

previous term

series

terms of a sequence being added together

partial sum of a geometric series

the sum of a limited number of terms of an infinite geometric sequence

Geometric Series

the sum of the terms of a geometric sequence

Dominant terms theory

the term that increases most quickly as n increases