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

 Let P(n) :
I.    For n = 1,
      P(1) : 1

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

∴     P(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 principle of mathematical induction, P(n) is true for all