Question

Check my answer please?

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

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

I began testing for n=1

4(1)=4

4(1)+2=6.

So it is false because it did not equal did not equal 4, correct?

Answer 1

Nono, you incorrectly calculated \(\large s_1\)

Answer 2

The sum is \[\huge \sum_{1}^{n} 4n * (4n+2)\]

Answer 3

Plug 1 in for n to figure out \(\huge s_1\)

Answer 4

24?

Answer 5

Yes. \(\huge S_1 = 4*6 = 24\)

Answer 6

Thanks. Then what do I do?

Answer 7

Check the right hand side of the equation. Find out if the equation is true for n=1.

Answer 8

I get that the right side is 60?

Answer 9

That's what I got.

Answer 10

so does that mean it is false?

Answer 11

Or actually, I got 50. But still, it didn't give us 24, like it should have.

Answer 12

Ok. I see what you mean. Thanks. I really appreciate your help.