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Summation

Summation. Summation notation. Gauss summation trick. Geometric series. Harmonic series. ( r < 1). Summation notation. a k. k 0 + 1. k 0 - 1. k 0. k f - 1. k f. k f + 1. k. Summation notation. a k. k 0 + 1. k 0 - 1. k 0. k f - 1. k f. k f + 1. k. Summation notation.

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Summation

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

  2. Summation notation ak k0+ 1 k0- 1 k0 kf- 1 kf kf+ 1 k

  3. Summation notation ak k0+ 1 k0 - 1 k0 kf- 1 kf kf+ 1 k

  4. Summation notation

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

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

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

  8. Geometric series Ark (zoom-out vertical scale) Ar0 r < 1 Ar1 Ar2 Ar3 Ar4 Ar5 Ar6 Ar7 k . . . 0 1 2 3 4 5 6 7

  9. Geometric series Ark Repeated addition seems to point toward a finite value r < 1 k . . . 0 1 2 3 4 5 6 7

  10. Geometric series Ark r < 1 k . . . 0 1 2 3

  11. Summation Summation notation Gauss summation trick Geometric series Harmonic series (r < 1)

  12. Harmonic series

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