Question

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

Answer 1

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

Answer 2

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

Answer 3

isn't the pattern supposed to be (n+3)(n+5)?

Answer 4

that was the question that was given to me so i wouldn't know

Answer 5

there is no such n that will give you 5(7) or 6(8) with 4n(4n+2) because 4n is a multiple of 4.
so it should have been 4(6) + 8(10) + 12(14) + ... + 4n(4n+2)

I would say false.

Answer 6

ok since its false i then have to show why its false

Answer 7

let n = 1, then sum is the first term 4(6) = 24

but when you plug 1 in for n [4(4n+1)(8n+7)]/6, you get 50

Answer 8

so it doesn't work for all positive integer

Answer 9

and that would be it?

Answer 10

I would say so, unless there is something that is supposed to be understood but was not explicitly stated in the question.