1. SUMMATION or SIGMA NOTATION
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2. DEFINITIONS Sigma Notation for Finite Sums
This symbol denotes the sum a1 + a an.
The a's are the terms of the sum: a1 is the first term, a2 is the second term, ak is the kth term, and an is the nth and last term.
The variable k is the index of summation.
The values of k run through the integers from 1 to n.
The number 1 is the lower limit of summation; the number n is the upper limit of summation.
Friday, February 15, 2019Friday, February 15, 2019
Mr M Kennedy

3. Write the sum without sigma notation. Then evaluate it.
EXAMPLE
Write the sum without sigma notation. Then evaluate it.
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Mr M Kennedy

4. SOLUTION Friday, February 15, 2019Friday, February 15, 2019
Mr M Kennedy

5. Write the sum without sigma notation. Then evaluate it.
EXAMPLE
Write the sum without sigma notation. Then evaluate it.
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Mr M Kennedy

6. SOLUTION Friday, February 15, 2019Friday, February 15, 2019
Mr M Kennedy

7. NOTE
The lower limit of summation does not have to be 1; it can be any integer. It is often simplest to start with k = 0 or k = 1.
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Mr M Kennedy

8. Express the sum 1 + 3 + 5 + 7 + 9 in sigma notation.
EXAMPLE
Express the sum in sigma notation.
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9. HERE ARE SEVERAL SOLUTIONS
Starting with k = 2:
Starting with k = -3:
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10. ...SOLUTION Starting with k = 0: Starting with k = 1:
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11. ALGEBRA RULES FOR FINITE SUMS...
Sum Rule:
Difference Rule:
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12. ...ALGEBRA RULES FOR FINITE SUMS Constant Multiple Rule:
Constant Value Rule:
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Mr M Kennedy

13. Constant Multiple Rule
EXAMPLE
Sum Rule
Constant Multiple Rule
Constant Value Rule
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14. Discovered by Gauss at age 5
The first n integers:
FAMOUS FINITE SUM FORMULAS
Discovered by Gauss at age 5
The first n squares:
The first n cubes:
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Mr M Kennedy

15. Use the algebra rules and the finite sum formulas to evaluate the sum.
EXAMPLE
Use the algebra rules and the finite sum formulas to evaluate the sum.
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Mr M Kennedy

16. Constant Multiple Rule
SOLUTION
Distribute the k.
Sum Rule and
Constant Multiple Rule
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Mr M Kennedy
Finite Sum Formulas