How To Calculate Harmonic Progression?

Short tutorial on how to calculate harmonic progression from arithmetic progression with formula and example.

Harmonic Progression Series and Formula

Harmonic Progression in mathematical geometry is a sequence of real numbers formed by taking the reciprocals of an arithmetic progression.
How To Calculate Harmonic Progression
Example: The sequence 1,2,3,4,5 is an arithmetic progression, so its reciprocals 1/1,1/2,1/3,1/4,1/5 are harmonic progression.
Harmonic Progression Series and Formula:
Harmonic Progression (H.P) = 1/a , 1/a+d, 1/a+2d, 1/a+3d.........1/a+kd

Where,
a is the starting number in the sequence
d is the common difference between the numbers given in the sequence.
Harmonic Progression Formula
Let us learn here how to calculate harmonic progression from arithmetic progression with a neat example.
Example: Consider the sequence of arithmetic progression 3,5,7,9,11. Calculate harmonic progression.
Given:
A.P = 3,5,7,9,11
Starting Sequence = 3
Common Difference = 2
Harmonic Progression Example
Solution:
Applying the values in the formula,
Harmonic Progression (H.P) = 1/3 , 1/3+2, 1/3+2(2), 1/3+3(2), 1/3+4(2)
Harmonic Progression (H.P) = 1/3 , 1/5, 1/7, 1/9, 1/11
Harmonic Progression Calculation


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