## 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. anonymous

$4\times6 + 5 \times7 +6\times8 +... + 4n(4n+2) = \frac{ 4(4n+1)(8n+7) }{ 6 }$

2. freckles

well first step is try to show it is true for n=1

3. anonymous

is n = 1 4? or 4x6

4. freckles

for n=1 you only have one term which is the 4*6 on the left hand side

5. anonymous

ok so I am trying to show that 24 = the fraction at the end there

6. freckles

yes for n=1

7. anonymous

ok, and if that doesnt = 24 then it is false, right?

8. freckles

right

9. anonymous

alright, I just didnt know if i was doing it right, Thank you for the help, I think thats all I need.

10. freckles

np

11. freckles

if the left side confuses you I can show you what the left side looks like for n=2

12. freckles

or even n=3

13. anonymous

I think i get it now, it was confusing cause it was 4 x 6, but now i realize that since it is a sum that the terms are seperated by +

14. freckles

ok cool stuff

15. anonymous

thanks for the help! :)