When `'n'` number of particles of masses `m, 2m, 3m,….nm` are at distances `x_1 =1, x_2 =4, x_3=9…x_n = n^2` units respectively from origin on the X-axis, then find the distance of centre of mass of the system from origin.

Explanation

`x_(cm) = (m(1)+2m(4)+3m(9)+...+nm(n^(2)))/(m_+2m+3m+....+nm)`
` (m(1+2^(3)+3^+....+n^(3)))/(m(1+2+3+....+n))`
`((n(n+1))/2)^(2)/((n(n+1))/2) = (n(n+1))/2 `