Harmonic Sequence Calculator

Calculate terms, sums, and properties of harmonic sequences (1/a, 1/(a+d), 1/(a+2d), ...).

Sequence Parameters

A harmonic sequence has terms 1/a, 1/(a+d), 1/(a+2d), ... where the reciprocals form an arithmetic sequence.

First Denominator (a)

Common Difference (d)

Number of Terms

Find Term Position

1/1=1.00001/2=0.50001/3=0.33331/4=0.25001/5=0.20001/6=0.16671/7=0.14291/8=0.12501/9=0.11111/10=0.1000

0.200000

= 1/(1 + 4 × 1)

2.928968

Harmonic Mean

0.181818

Standard H_10

2.928968

First Term

1/1 = 1.0000

The denominators form an arithmetic sequence:

12345678910

General Term

h_n = 1/(a + (n-1)d)

Harmonic Mean

HM = n/(1/a_1 + 1/a_2 + ... + 1/a_n)

Standard Harmonic Number

H_n = 1 + 1/2 + 1/3 + ... + 1/n

Approximation

H_n ≈ ln(n) + γ (Euler-Mascheroni)