Get Math Help

GET TUTORING NEAR ME!

(800) 434-2582

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Home / Get Math Help

    Harmonic Progression

    Basic definition

    The harmonic series is the slowly divergent sum of the reciprocals of all positive integers.

    Detailed definition

    The series
 sum_(k = 1)^∞ 1/k
is called the harmonic series. It can be shown to diverge using the integral test by comparison with the function 1/x. The divergence, however, is very slow. Divergence of the harmonic series was first demonstrated by Nicole d'Oresme (ca. 1323-1382), but was mislaid for several centuries (Havil 2003, p. 23; Derbyshire 2004, pp. 9-10). The result was proved again by Pietro Mengoli in 1647, by Johann Bernoulli in 1687, and by Jakob Bernoulli shortly thereafter.

    Educational grade level

    college level (AP calculus BC)

    Back to List | POWERED BY THE WOLFRAM LANGUAGE