Harmonic Series Calculator

Summary

Enter a positive integer n to compute H_n = 1 + 1/2 + ... + 1/n with a step-by-step term table.

How it works

1. Enter a positive integer n (up to 10,000).
2. The calculator adds 1/k for each k from 1 to n.
3. A table shows every term, its decimal value, and the running sum.
4. The final result H_n is displayed with high precision.
5. Use the Copy button to copy the result to your clipboard.

Use cases

• Verify harmonic series convergence in math coursework.
• Explore how slowly H_n grows (it diverges, but very slowly).
• Check specific partial sums for number theory proofs.
• Visualize the diminishing contribution of each term.
• Understand the Euler-Mascheroni constant approximation.
• Compare H_n against ln(n) + γ estimates.

Frequently Asked Questions