Mathmatical induction (with question)

Question

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

 

1² + 4² + 7² + ... + (3n - 2)² = 

Answer 1

 

quantity n times six n squared minus three n minus one all divide by two.

Mathematical induction is a special way of proving things.

It has only two steps.

Step - 1) Statement is true for n = 1

Step - 2) one part being assume the statement is true for n =  k

prove the statement is true for " k + 1"

Check the equation for n = 1

Left hand side

                

                

Right hand side

                               

                              

For n = 1, the statement is true.

• Assume the statement is true for n =  k

• Now, prove the statement is true for " k + 1".

For n = k + 1

The statement is ---> (1)

We need to the prove the equation (1).

 

Answer 2

Contd...

 Add on each side.

Therefore, by the mathematical induction the statement is true.