SECTION 1.6 SIGMA NOTATIONSAND 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 consecutivesquares, cubes, and powers
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I) WHAT IS A SIGMA NOTATION:
A notation that represents a series (sum)
Function
Variable in thefunction
The value of “k”
in the last term
The value of “k”
in the first term
Note: The number of terms will be (b – a + 1)
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EX: EXPAND AND EVALUATE THE FOLLOWING SERIES:
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When a sigma notation contain too many terms, use theformulas from the Geometric series to find the sum
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PRACTICE: EVALUATE EACH OF THE FOLLOWINGINFINITE GEOMETRIC SERIES:
Since:
the infinite geometric series will
become infinity
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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 placean index for the number of terms above the notation
Start with n=1
There are 8 terms
EX: GIVEN THE FOLLOWING GEOMETRIC SERIES, REWRITEAS 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