Mathematical Induction

Prove that 1·1!+2·2!+···+n·n!=(n+1)!−1 whenever n is a positive integer. 

Mathematical Induction /

As usual, we start with the definitions. PRINCIPLE OF MATHEMATICAL INDUCTION To prove that P(n) is true for all positive integers n, where P (n) is a propositional function, we complete two steps: The definition above is from the textbook Discrete Mathematics and its Applications by Rosen. Now we can solve the exercise by completing […]

Prove that 1·1!+2·2!+···+n·n!=(n+1)!−1 whenever n is a positive integer.  Read More »

Prove that 1^2 +3^2 +5^2 +···+(2n+1)^2 =(n+1) (2n + 1)(2n + 3)/3 whenever n is a nonnegative integer

Mathematical Induction /

Let’s revisit the principle of mathematical induction. PRINCIPLE OF MATHEMATICAL INDUCTION To prove that P(n) is true for all positive integers n, where P (n) is a propositional function, we complete two steps: The definition above is from the textbook Discrete Mathematics and its Applications by Rosen. Now, let’s solve the exercise. As the principle

Prove that 1^2 +3^2 +5^2 +···+(2n+1)^2 =(n+1) (2n + 1)(2n + 3)/3 whenever n is a nonnegative integer Read More »