April 19, 2017
Aim #90: How do we use sigma notation?
Do Now: What is the sum of the first fifty terms of the sequence an = 4n ­ 1?
Sigma Notation
The Greek capital letter sigma, Σ, is used to indicate a sum, or summation. Key Symbols:
Ʃ ­ sigma ­ summation notation
.
rule summand ­ index ­
(often the letters i, k or n)
Example 1) Represent each of the following sums using summation notation. a) the sum of the first 50 terms of the sequence 3, 6, 9, 12, 15...
b) the sum of the first 17 terms of the sequence 36, ­18, 9, ­4.5,...
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Practice
Evaluate the following sums:
1)
2)
3)
4)
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5) Evaluate
6) If x1 = 19, x2 = 20, x3 = 26, x4 = 30, and , find the value of x5. 5) Using sigma notation, write an expression that indicates the sum below. 800, 200, 50, ... , .78125
6) Using sigma notation, write an expression that indicates the sum below. Sum it UP
To represent the sum of the terms of a sequence, we can use sigma notation.
index that we end with
index that we start with
To find the number of terms, subtract the index numbers and add 1
To write a series in sigma notation, create an explicit formula and think about the index values!
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