Noun
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harmonic number (plural harmonic numbers)
(number theory) Any of a series of numbers formed from the sum of the reciprocals of consecutive natural numbers
The fourth harmonic number has a value of
H
3
=
∑
k
=
1
3
1
k
=
1
1
+
1
2
+
1
3
=
1
5
6
.
{\displaystyle H_{3}=\sum _{k=1}^{3}{\frac {1}{k}}={\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}=1{\frac {5}{6}}.}