1. Sequences and Summations
Elementary Discrete Mathematics
Jim Skon

2. Sequences and Summations
Consider the function ƒ: N+  R where ƒ(x) = 1/x Then:
The image of this function can be said to form a sequence:
Sequences and Summations

3. Sequences and Summations
Sequence: A sequence is a function from a subset of the set of integers to a set S.
The image of the nth integer is denoted by an.
an is called a term of the sequence.
Then, for the function above, we can define the sequence as:
Sequences and Summations

4. Sequences and Summations
The terms of this the previous sequence are:
a1, a2, a3, a4, a5, a6,...
Which is:
Where:
Sequences and Summations

5. Sequences and Summations
Again, if the sequence is defined as:
Then
and so on...
Sequences and Summations

6. Sequences and Summations
Sequence Examples
Sequences and Summations

7. Sequences and Summations
Summation Notation
Symbolic way to define the sum of a series.
Example:
i - index of summation
1 - lower limit of summation
upper limit of summation
Sequences and Summations

8. Summation Notation Examples
Sequences and Summations

9. Summation Notation Examples
Where S = {1, 2, 3, 4, 5}
f:RR
f(x) = 3x2+1
Sequences and Summations