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

Let
I.      For n = 1,
       is true.
II.    Suppose the statement is true for n = m,
   
          i.e.,     ... (i)
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 mathematical induction, P(n) is true for all