When `'n'` number of particles of masses `m, 2m, 3m,….nm` are at distances `x_1 =1, x_2 =2, x_3=3…x_n = n` units respectively from origin on the X-axis, then find the distance of centre of mass of the system from origin.

Explanation

To find the distance of the center of mass of a system of particles with masses \( m, 2m, 3m, \ldots, nm \) located at distances \( x_1 = 1, x_2 = 2, x_3 = 3, \ldots, x_n = n \) from the origin on the X-axis, we can follow these steps:

### Step 1: Understand the formula for the center of mass
The center of mass \( x_{cm} \) of a system of particles is given by the formula:
\[ x_{cm} = \frac{\sum (x_i m_i)}{\sum m_i} \]
where \( x_i \) is the position of each particle and \( m_i \) is the mass of each particle.
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