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Understanding Sequences and Summation Notation

This module covers key concepts in sequences and summation notation. It defines sequences as ordered sets of numbers and explores recursively-defined sequences, such as the Fibonacci sequence. You will learn how to find terms of sequences by detecting patterns, compute partial sums, and use summation notation (sigma notation) to express sums. The discussion emphasizes practical understanding at an 85% mastery level through hands-on practice and application of concepts. Enhance your mathematical skills in sequences and series with engaging exercises.

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Understanding Sequences and Summation Notation

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  1. 10.1: Sequences and Summation Notation TSW understand the definition and notation of sequences, understand recursively- defined sequences, including the Fibonacci sequence, and understand partial sums, including summation notation at an 85% mastery level as demonstrated by discussion and practice.

  2. Definition of Sequence A sequence is a set of numbers written in a specific order: a1, a2, a3, … , an A sequence is also a function f whose domain is the set of natural numbers. The values f (1), f (2), f (3),… are called the terms.

  3. Finding Terms of a Sequence

  4. Detecting Patterns

  5. Recursively Defined Sequences

  6. Partial Sums of a Sequence

  7. Partial Sums

  8. Sigma Notation

  9. Sigma Notation

  10. Properties of Sums

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