Mathematical Induction Part I

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1. Mathematical Induction  part I  ( Prove that 1+2+3+...+n=n(n+1)/2 by inductionfor all n in the set of natural numbers )

2. Mathematical Induction  part II (Prove that 5^n-2^n is divisible by 3 for all n in the set of natural numbers)

3. Mathematical Induction  part III (Prove that  1+5+9+...+(4n-3)=n(2n-1) for all n in the set of natural numbers)

4. Mathematical Induction  part IV  ( Prove that 8^n-1 is divisible by  7 for all n in the set of natural numbers)

5. Mathematical Induction Part V  (Prove that n^3+2n is divisible by 3  for all n in the set of natural numbers)

6. Mathematical Induction Part VI ( Prove that n^2 is less than or equal to 2  for all n in the set of natural numbers)

7. Mathematical Induction Part VII  (Prove that 8^n-1 is divisible by  7 for all n in the set of natural numbers)

8.  Proof by Mathematical induction Part VIII   (Prove that 1+3+5+7..=n^2  for all n in the set of natural numbers)

 9. Proof by induction Part IX  IX Prove that Σ k^2= n(n+1)(2n+1)/6 discrete principle

10.  Proof by induction Part X  prove 1+5+9+13+ +(4n-3)=n(4n-2)/2