Difference between revisions of "Manuals/calci/HARMONICSERIES"

Latest revision as of 14:40, 28 November 2018

HARMONICSERIES (Start,Numbers,OnlyNth)

This sfunction displays the Harmonic series of the numbers.
A series is an expression with an infinite number of terms, like this: $\sum _{n=1}^{\infty }{\frac {1}{n}}=1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+....$
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.

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 ==Description==
 *This sfunction displays the Harmonic series of the numbers.
-*A series is an expression  with an infinite number of terms, like this:\sum_{n=1}^{/infty} \frac{1}{n} = 1+ \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....
+*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.
 *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==
+#HARMONICSERIES(3,10,4) = 0.3333333333333333
+#HARMONICSERIES(189,20,18) = 9.947368421052632
+==Related Videos==
+{{#ev:youtube|v=OqBZCycIYfw|280|center|Harmonic Series}}
+==See Also==
+*[[Manuals/calci/HARMEAN| HARMEAN]]
+*[[Manuals/calci/SUM  | SUM ]]
+==References==
+[https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)  Harmonic series]
+*[[Z_API_Functions | List of Main Z Functions]]
+*[[ Z3 |   Z3 home ]]