When `n` number of particles each of mass `m` are at distances `x_(1)=1, x_(2)=2, x_(3)=3, ………., x_(n)=n` units from origin on the x-axis, then find the distance of their centre of mass from origin.

Explanation

`x_(cm)=(m(1)+m(2)+m(3)+......+m(n))/(m+m+m+.......+m(n" terms"))`
`=(m(1+2+3+......+n))/(nm)=(m((n(n+1))/(2)))/(nm)`
`x_(cm)=(n+1)/(2)`