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)+...+mn(n^(2)))/(m+2m+3m+...+nm)`
`=(m(1+2^(3)+3^(3)+...+n^(3)))/(m(1+2+3+...+n))=(((n(n+1))/2)^(2))/((n(n+1))/2)=(n(n+1))/2`