Manuals/calci/HARMONICSERIES

HARMONICSERIES (Start,Numbers,OnlyNth)

• $Start$ are any positive integer .
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Numbers} is the number of the series.
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle OnlyNth } 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:Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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.

Examples

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

Related Videos

Harmonic Series

See Also

• HARMEAN
• SUM

References

Harmonic series

• List of Main Z Functions

• Z3 home