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

Let
I.       For n = 2(note this step, n>1)
       

        which is true

∴       P(n) is true for n = 2
II.      Suppose the statement is true for n = m,
                         .... (i)
III.      For n = m + 1,
         
or     
or      
         Adding on both sides of (i), we get
 
        
    
     
     
         But,

∴     

∴         P (m + 1) is true
∴         P(m) is true P(m + 1) is true
Hence, P(n) is true for all