Math 111 - 11/28/11

8.1 Intro to sequences, series, summation notation...

A "Sequence" is a set of numbers in some specific order

Ex:

{1,2,3,4,5,...}

{2,4,6,8,10,...}

{5,10,15,20,...}

{0,0,0,0,0,...}

{1,11,21,1211,543,8,-7...}

A sequence can be infinite (like all of the above)

or finite

Ex

{1}

{5,3,1}

{2,2,222}

And no specific pattern is required (but there usually is one anyway).

The numbers in a sequence are called its "terms" and we use subscripts to refer to them...

b = {1,11,21,1211,543,8,-7...}

If a sequence has the right pattern, you can a write a formula for the terms...

For example

Has the formula

{1,2,3,4,5,...}

{5,10,15,20,...}

{0,0,0,0,0,...}

So I could tell you

A "series" is a sum of the beginning of a sequence...

Ex:

The "first partial sum" is

The "second partial sum" is

The "third partial sum" is

The 6th partial sum is

These make a sequence of their own... this is a series (the sums of a sequence)

Summation notation:

We use a greek capitol sigma to represent sums...

Ex:

means

Ex:

Ex:

Ex:

Series vs. sequence...

is a sequence

are the partial sums of that sequence

so

but