Use mathematical induction to prove 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 understand how to prove it by mathematical induction for the most part, I just don't understand how the sequence can possibly go from multiplying to adding and back again.

Question

Use mathematical induction to prove 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 understand how to prove it by mathematical induction for the most part, I just don't understand how the sequence can possibly go from multiplying to adding and back again.

amistre64 · Answer

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

anonymous · Answer

Oh gosh. That makes sense now. There was nothing pointing to that through all the material I reviewed.

amistre64 · Answer

4(4+2) = (4(4+1)(8+7))/6

24 = 50 is not trtue

anonymous · Answer

Yes. This makes much more sense now. Thank you!