Prove the following by using the principle of mathematical induction for all

.

Let P(n):
I.     For n =1,
     
∴     P(1) is true.
II.   Suppose the statement is true for n = m,

∴   
III.   For n = m + 1,
       
                                                                        
or     1.2.3 + 2.3.4 + 3.4.5 + ........... + m (m + 1) (m + 2) + (m + 1) (m + 2) (m + 3)
                                                                          
        From (i), 1.2.3 + 2.3.4 + 3.4.5 + ......... + m (m + 1) (m + 2)
                                                                       

∴   
                                                                          

       
             which is true.

∴        P(m + 1) is true.

∴        P(m) is true P(m + 1) is true.
Hence, by the principle of mathematical induction, P(n) is true for all