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

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

∴          .... (i)

III.   For n = m + 1,
       P(m + 1):
or    
        From (i),
      

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