Prove the following by principle of mathematical induction for all :

Let
I.     For n = 1,
     

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

∴    
III.  For n = 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 principle of mathematical induction, P(n) is true for all