Mention the expression for position coordinates of mass of a) n Particle system b) a rigid body c) and a uniform thin rod

Let we have 'n' particles of masses m₁, m₂----m_n respectivley, along a straight line.
Then the position of the centre of mass of the system of particles is given by
$X=\frac{m_1{x}_1+m_2{x}_2------m_n{x}_n}{m_1+m_2------m_n}=\frac{{\displaystyle \sum _{i=1}^n}{m}_i{x}_i}{M}$
similarly $Y=\frac{\sum _{i=1}^n{m}_i{y}_i}{M},Z=\frac{\sum _{i=1}^n{m}_i{z}_i}{M}$
(ii) A rigid body is a system of closely packed particles then the coordinates of the centre of mass are then given by
$X=\frac{{\displaystyle \sum _{i=1}^n}(∆m_i)x_i}{{\displaystyle \underset{}{\overset{}{\sum ∆m}}}}$_i where∑∆m_i=∫dm=MX=1m∫xdm, similarly Y=1m∫ydm, Z=1m∫zdm 
(iii) the centre of mass of uniform thin rod lies at their geometric centres.