Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
medal!!!!!
@ganeshie8

Question

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
medal!!!!!
@ganeshie8

anonymous · Answer

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

anonymous · Answer

@SithsAndGiggles do you know this?

anonymous · Answer

@hartnn

anonymous · Answer

I've done my share of induction proofs, yes. Give me a moment

anonymous · Answer

please show all steps so i understand it

anonymous · Answer

okay thanks(: @SithsAndGiggles

anonymous · Answer

What happens when $n=1$?

anonymous · Answer

i dont know:(

anonymous · Answer

What I'm asking is, "is this true?"
$$(4\cdot1)(4\cdot1+2)=\frac{4(4\cdot1)((8\cdot1)+7)}{6}$$

anonymous · Answer

no it is false

anonymous · Answer

Okay, so if the formula above doesn't hold for $n=1$, then it's certainly true that it does not hold for ALL natural numbers. What does that tell you? Is the formula correct?

anonymous · Answer

since it is false, it is not correct

anonymous · Answer

Right. The counter-example is $n=1$, so the statement/formula is false.

anonymous · Answer

so wait since it is false all i have to do is write that it is false? it shows to prove that the statement is false... how to i do that?

anonymous · Answer

nevermind, i understand(: thanks!

anonymous · Answer

yw