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

Question

anonymous · Answer

$$4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n (4n+2) = \frac{ 4(4n+1) (8n+7) }{ 6 }$$

anonymous · Answer

When I substitute n for 1 I don't get the same amount on both sides?

anonymous · Answer

@precal @matricked

amistre64 · Answer

then what does that tell you about the proof?

amistre64 · Answer

hint:  show why it doesnt work ...

anonymous · Answer

Oh, so that's it? I just show that it doesn't work.

anonymous · Answer

I'm sorry openstudy wouldn't load. I'm going to show you what I have written down and could you tell me if it's right or not?

amistre64 · Answer

thats all there is to it yes.  its asking you to show it works, or show why it doesnt.

since n=1 fails, then this doesnt work.

anonymous · Answer

$$4(1)(4(1)+2) = 4(4(1)+1)(8(1)+7)$$

24 = 300 

it doesn't equal so therefore it can't be be proven? or is it false or something?