Search for a tool
Harmonic Number

Tool for calculating the values of the harmonic numbers, ie the values of the nth partial sums of the harmonic series as well as their inverse. The harmonic series is the series of inverses of natural non-zero integers. 1 + 1/2 + 1/3 + ... + 1/n

Results

Harmonic Number -

Tag(s) : Series

Share
Share
dCode and you

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!


Please, check our community Discord for help requests!


Thanks to your feedback and relevant comments, dCode has developped the best Harmonic Number tool, so feel free to write! Thank you !

Harmonic Number

Nth Harmonic Number Calculator

H(N) = 1+1/2+1/3+...+1/N


Reciproqual Harmonic Value


Tool for calculating the values of the harmonic numbers, ie the values of the nth partial sums of the harmonic series as well as their inverse. The harmonic series is the series of inverses of natural non-zero integers. 1 + 1/2 + 1/3 + ... + 1/n

Answers to Questions

How to calculate an harmonic number?

Harmonic numbers are described by the formula: (sum of inverses of natural numbers)

$$ H_n = \sum_{k=1}^n \frac{1}{k} = 1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n} $$

Example: $ H_3 = 1+\frac{1}{2} = \frac{3}{2} = 1.5 $

The following recurrence formula can also be applied to get a series:

$$ H_n = H_{n-1} + \frac{1}{n} $$

$ H_n $ is called the Harmonic series.

When $ n $ is very big, the following approximation using logarithm can be applied

$$ \lim_{n \to \infty} H_n = \ln n + \gamma $$

with $ \gamma \approx 0.577215665 $ the Euler–Mascheroni constant.

What are the first values of the Harmonic Series?

The first harmonic numbers are:

nH(n)≈H(n)
11/11
23/21.5
311/61.83333
425/122.08333
5137/602.28333
649/202.45
7363/1402.59286
8761/2802.71786
97129/25202.82896
102.92897
1005.18738
10007.48547
100009.78761
10000012.09015
100000014.39272
1000000016.69531
10000000018.99790
100000000021.30048

Source code

dCode retains ownership of the online 'Harmonic Number' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Harmonic Number download for offline use on PC, tablet, iPhone or Android !

Need Help ?

Please, check our community Discord for help requests!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developped the best Harmonic Number tool, so feel free to write! Thank you !


Source : https://www.dcode.fr/harmonic-number
© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback