Use Mathematical Induction to show the follwing statements are correct.

[RatherBadAtMath]

Hi everyone I have solved question 1 but not quite sure of question 2 as when n=1 in base case it is not valid and am not sure how to continue. Any help would be greatly appreciated.

 

[yoscar04]

View attachment 20540

Hi everyone I have solved question 1 but not quite sure of question 2 as when n=1 in base case it is not valid and am not sure how to continue. Any help would be greatly appreciated.

Why do you think (ii) is not valid for n=1?
If you substitute n=1 you get 5 in both sides. Now to continue assume it is true for n and then try to see it is also true for n+1.

 

[RatherBadAtMath]

Thank you for the reply.

I substituted in n=1 into both sides

2(1)^2 = 1(2(1)+ 1) (4(1) + 1)/ 3

The left side equals 4 and then right side of the equation is 5. I am not quite sure as to how both sides can equal 5.

 

[yoscar04]

Thank you for the reply.

I substituted in n=1 into both sides

2(1)^2 = 1(2(1)+ 1) (4(1) + 1)/ 3

The left side equals 4 and then right side of the equation is 5. I am not quite sure as to how both sides can equal 5.

1²+(2*1)²=5
1*(2*1+1)*(4*1+1)/3=5