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Summation 1 Summation notation Geometric seriesHarmonic series Gauss summation trick (r < 1)

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Presentation on theme: "Summation 1 Summation notation Geometric seriesHarmonic series Gauss summation trick (r < 1)"— Presentation transcript:

1 Summation 1 Summation notation Geometric seriesHarmonic series Gauss summation trick (r < 1)

2 2 Summation notation akak k k0k0 kfkf k k k f + 1 k f - 1

3 3 Summation notation akak k k0k0 kfkf k k k f + 1 k f - 1

4 4 Summation notation

5 Summation 5 Summation notation Geometric seriesHarmonic series Gauss summation trick (r < 1)

6 6 Gauss summation trick 2 Figure it out: Why N + 1 individuals? Why not N ?

7 Summation 7 Summation notation Geometric seriesHarmonic series Gauss summation trick (r < 1)

8 8 Geometric series Ar k k Ar 0 Ar 1 Ar 2 Ar 3 Ar 4 Ar 5 Ar 6 Ar 7 r < 1 (zoom-out vertical scale)

9 9 Geometric series Ar k k r < 1 Repeated addition seems to point toward a finite value

10 10 Ar k k r < 1 Geometric series

11 11 Geometric sum: Summation notation Ar k k r < 1 Use j := k – 1 to check this last step STOP

12 Summation 12 Summation notation Geometric seriesHarmonic series Gauss summation trick (r < 1)

13 13 Harmonic series


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