By the Principle of Mathematical Induction, prove the following for all n `in` N :
`(1+1/1)(1+1/2)(1+1/3)....... (1+1/n) =(n+1)`.

By Principle of Mathematical Induction, prove that : 2^n >n for all n in N.

By the Principle of Mathematical Induction, prove the following for all n in N : 1/1.3+1/3.5+1/5.7+......+ 1/((2n -1)(2n +1))= n/(2n +1) .

By the Principle of Mathematical Induction, prove the following for all n in N : 4+8+ 12+......+ 4n= 2n(n + 1) .

By the Principle of Mathematical Induction, prove the following for all n in N : 15^(2n-1)+1 is multiple of 16.

By using the Principle of Mathematical Induction, prove the following for all n in N : 1/2+1/4+1/8+..........+1/2^n =1- 1/2^n .

By the Principle of Mathematical Induction, prove the following for all n in N : 2^(3n)-1 is divisible by 7 .

By the Principle of Mathematical Induction, prove the following for all n in N : 3^(2n)-1 is divisible by 8 .

By the Principle of Mathematical Induction, prove the following for all n in N : 5^(2n)-1 is divisible by 24.

By using the Principle of Mathematical Induction, prove the following for all n in N : 1.1! +2.2! +3.3! +.......+ n.n! = (n+1)!-1 .

By the Principle of Mathematical Induction, prove the following for all n in N : a^(2n-1)-1 is divisible by a-1.