Section 1.6 Sigma Notations and Summation

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Presentation transcript:

Section 1.6 Sigma Notations and Summation i) Concept of Sigma Notation, number of terms ii) Solving for Sums using Sigma Notations iii) Problems involving Sigma Notations iv) Sums of Sequences involving consecutive squares, cubes, and powers © Copyright all rights reserved to Homework depot: www.BCMath.ca

I) What is a Sigma Notation: A notation that represents a series (sum) The value of “k” in the last term Function Variable in the function The value of “k” in the first term Note: The number of terms will be (b – a + 1) © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: Expand and Evaluate the following Series: © Copyright all rights reserved to Homework depot: www.BCMath.ca

When a sigma notation contain too many terms, use the formulas from the Geometric series to find the sum © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: Evaluate the following Series: © Copyright all rights reserved to Homework depot: www.BCMath.ca

Practice: Evaluate each of the following infinite Geometric series: Since: the infinite geometric series will become infinity © Copyright all rights reserved to Homework depot: www.BCMath.ca

Converting a Series to Sigma Notation Form Find a formula for the general term tn If the series is arithmetic use: If the series is geometric use: Count the number of terms, start with n=1 and then place an index for the number of terms above the notation Start with n=1 There are 8 terms

EX: Given the following Geometric Series, rewrite as a sigma Notation: This is an arithmetric series Start with n=1 There are 9 terms This is a geometric series Start with n=1 There are 6 terms

Homework: Assignment 2.5