Study Online Harmonic Progression Help

Introduction to study online harmonic progression help:

A harmonic progression is a series of numbers that are all obtained by taking the inverse of the arithmetic progression. Hence it is necessary to find the arithmetic progression for calculating the harmonic progression. Let us solve some of the example explaining arithmetic progression.When student have doubt in study, they come to online for their help. The tutors will help the students to clarify the doubts in study through online white board.

Formula for Study Online Harmonic Progression Help:

The general form of the harmonic progression is given by,

`a, a/(1+d), a/(1+2d),a/(1+3d), a/(1+4d), ....`

These terms are all the inverse of the arithmetic progression.

nth term of harmonic progression  is given  by,

`T_n =1/( a + (n - 1)d)`

Where

a is the first term

d is the common difference between the successive numbers.

The harmonic mean of two numbers a and b are,

` (2ab)/(a+b)`

The harmonic mean of three numbers a, b and c are,

`(3abc)/(ab+bc+ac)`         

Similarly, the harmonic mean of two numbers a and b are,

`n/(1/a + 1/b + 1/c +. . . 1/N)`

Example Problems for Study Online Harmonic Progression Help:

Example 1:

Find the harmonic progression up to fourth term with difference is 4 and the series starts from 3.

Solution:

Step 1: The given terms are

a = 3;

d = 4;

Step 2:  Find Harmonic progression.

Step 3: Formula for harmonic progression is given by,

`1/a, 1/(a+d), 1/(a+2d),1/(a+3d), 1/(a+4d),...`

Step 4: on applying the all values we get,

= `1/3, 1/(3 + 4), 1/(3+2xx4), 1/(3+3xx4)` ,…

= `1/3, 1/7, 1/11, 1/15` ,…

= 0.333, 0.143, 0.091, 0.067,...

This is the harmonic progression series.

Example 2:

Find the harmonic progression up to fourth term with difference is 4 and the series starts from 2.

Solution:

Step 1: The given terms are

a = 2;

d = 4;

Step 2:  Find Harmonic progression.

Step 3: Formula for harmonic progression is given by,

`1/a, 1/(a+d), 1/(a+2d),1/(a+3d), 1/(a+4d),...`

Step 4: on applying the all values we get,

=` 1/2, 1/(2 + 4), 1/(2+2xx4), 1/(2+3xx4),...`

= `1/2, 1/6, 1/10, 1/14,...`

= 0.5, 0.167, 0.1, 0.017,...

This is the harmonic progression series.

Example 3:

Find the harmonic progression up to fourth term with difference is 4 and the series starts from 1.

Solution:

Step 1: The given terms are

a = 4;

d = 2;

Step 2:  Find Harmonic progression.

Step 3: Formula for harmonic progression is given by,

`1/a, 1/(a+d), 1/(a+2d),1/(a+3d), 1/(a+4d),...`

Step 4: on applying the all values we get,

= `1/1, 1/(1 + 4), 1/(1+2xx4), 1/(1+3xx4),...`

= `1/1, 1/5, 1/9, 1/13,...`

= 1, 0.2, 0.111, 0.077...

This is the harmonic progression series.