How this calculation works
Each new term adds 1/n. The sum grows slowly but is unbounded as n increases.
THE FORMULA
Hₙ = Σ 1/k, k = 1,…,nA worked example
H₄ = 1 + 1/2 + 1/3 + 1/4 = 25/12.
Good to know
The output is a floating-point approximation.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Sum reciprocals of consecutive positive integers.
The primary result is labeled “Harmonic number”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The output is a floating-point approximation.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
H₄ = 1 + 1/2 + 1/3 + 1/4 = 25/12.
Which rule does this calculator apply?
Hₙ = Σ 1/k, k = 1,…,n