Question

WILL AWARD MEDALS

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

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

Answer 1

@gurrilabill @Shay17 Can you guys help me out?

Answer 2

input (k+1) where the n is and it will help you figure it out
i had that same question :)

Answer 3

first, what is your basis step?

Answer 4

... is true for all positive integers n,
or show why it is false.

since positive integers are: 1,2,3,4,5,....

is this true for n=1?

Answer 5

try it out:

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

4(6) = 4(5)(15)/6

6 = 5(15)/6

36 = 5(15)

36 = 50+25, is that a true statement?

Answer 6

It's false.

Answer 7

So my answer is false? Or do I need to take further steps? @amistre64

Answer 8

... is true for all positive integers n,
or show why it is false.

since it is not true for at least one positive integer (n=1), then we have proven it to be false.

Answer 9

there is no need to continue to try proving it true when it is false from the start .... wouldnt you agree?

Answer 10

Yes, I agree (: Thank you so much for your help!