Difference between revisions of "Manuals/calci/HARMONICSERIES"

 
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==Description==
 
==Description==
 
*This sfunction displays the Harmonic series of the numbers.
 
*This sfunction displays the Harmonic series of the numbers.
*A series is an expression  with an infinite number of terms, like this:<math>\sum_{n=1}^{/infty} \frac{1}{n} = 1+ \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....</math>
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*A series is an expression  with an infinite number of terms, like this:<math>\sum_{n=1}^{\infty} \frac{1}{n} = 1+ \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....</math>
 
*This is the divergent infinite series.
 
*This is the divergent infinite series.
 
*In HARMONICSERIES(Start,Numbers,OnlyNth),Start is the beginning number of the series, Numbers is number of the number in the series and OnlyNth is the nth term of the Harmonic Series.
 
*In HARMONICSERIES(Start,Numbers,OnlyNth),Start is the beginning number of the series, Numbers is number of the number in the series and OnlyNth is the nth term of the Harmonic Series.
 
*Every term of the series after the first is the harmonic mean of the neighboring terms.
 
*Every term of the series after the first is the harmonic mean of the neighboring terms.
 
*The phrase harmonic mean likewise derives from music.
 
*The phrase harmonic mean likewise derives from music.
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==Examples==
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#HARMONICSERIES(3,10,4) = 0.3333333333333333
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#HARMONICSERIES(189,20,18) = 9.947368421052632
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==Related Videos==
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{{#ev:youtube|v=OqBZCycIYfw|280|center|Harmonic Series}}
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==See Also==
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*[[Manuals/calci/HARMEAN| HARMEAN]]
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*[[Manuals/calci/SUM  | SUM ]]
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==References==
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[https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)  Harmonic series]
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 15:40, 28 November 2018

HARMONICSERIES (Start,Numbers,OnlyNth)


  • are any positive integer .
  • is the number of the series.
  • is the Nth term of the series.

Description

  • This sfunction displays the Harmonic series of the numbers.
  • A series is an expression with an infinite number of terms, like this: 
  • This is the divergent infinite series.
  • In HARMONICSERIES(Start,Numbers,OnlyNth),Start is the beginning number of the series, Numbers is number of the number in the series and OnlyNth is the nth term of the Harmonic Series.
  • Every term of the series after the first is the harmonic mean of the neighboring terms.
  • The phrase harmonic mean likewise derives from music.

Examples

  1. HARMONICSERIES(3,10,4) = 0.3333333333333333
  2. HARMONICSERIES(189,20,18) = 9.947368421052632

Related Videos

Harmonic Series

See Also

References

Harmonic series