## anonymous one year ago 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) =

1. geerky42

4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) $$\textbf=$$ ??? what?

2. anonymous

it doesnt say... thats how it was written

3. zzr0ck3r

ouch

4. zzr0ck3r

it is not a statement...

5. geerky42

we cannot prove expression "4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2)"

6. geerky42

I mean it doesn't make sense.

7. anonymous

thats what i thought

8. zzr0ck3r

I cant find the formula elsewhere.

9. geerky42

What I realize though is that pattern is supposed to be $$n(n+2)$$ starting at $$n=4$$, not $$4n(4n+2)$$ Because otherwise pattern is supposed to be $$4\cdot6+8\cdot10+12\cdot14+\cdots$$

10. anonymous

okay i found it. 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = (4(4n+1)(8n+7))/6

11. zzr0ck3r

right @geerky42

12. zzr0ck3r

Do you want to see if it matches the formula she found?

13. geerky42

Maybe I misinterpreted the pattern, it's just $$\displaystyle \sum_{i=4}^{4n}i(i+2)$$ ?

14. anonymous

wait i found the answer since the statement is false. thank you though