Mathmatical induction 1

Question

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
(4 points each.)

1. 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = 

Answer 1

quantity four times quantity four n plus one times quantity eight n plus seven divided all divided by six.

Mathematical induction is a special way of proving things.

It has only two steps.

Step - 1) Statement is true for n = 1

Step - 2) If statement is true for n = k then n = k + 1 also true.

Check the equation for n = 1

Left hand side

                   

                   

                    

Right hand side

                                   

                                 

                                  

For n = 1 it is false.

By mathmetical induction the statement is false.