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What is Harmonic Progression ? What is Harmonic Series ? Is there any formula to find sum to 'n' terms in a harmonic progression ?

Asked by 28th January 2012, 7:48 PM
Answered by Expert

In mathematics, a harmonic progression is a progression formed by taking the reciprocals of an arithmetic progression. In other words, it is a sequence of the form

where ?1/d is not a natural number.

the harmonic series is the divergent infinite series:

Every term of the series after the first is the harmonic mean of the neighboring terms.

There isn't a good closed form expression. As a special case, one has the Harmonic numbers

There isn't even a good closed form expression for this particular sum, although there is a good approximation

where is the Euler-Mascheroni constant. Similar approximations can be given for more general sums of harmonic progressions.
Answered by Expert 29th January 2012, 8:05 PM
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