Sequences and Summations Elementary Discrete Mathematics Jim Skon

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

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

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

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

Sequences and Summations Sequence Examples Sequences and Summations

Sequences and Summations Summation Notation Symbolic way to define the sum of a series. Example: i - index of summation 1 - lower limit of summation 100 - upper limit of summation Sequences and Summations

Summation Notation Examples Sequences and Summations

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