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

Question

wampominater · Answer

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

freckles · Answer

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

wampominater · Answer

is n = 1 4? or 4x6

freckles · Answer

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

wampominater · Answer

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

freckles · Answer

yes for n=1

wampominater · Answer

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

freckles · Answer

right

wampominater · Answer

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

freckles · Answer

np

freckles · Answer

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

freckles · Answer

or even n=3

wampominater · Answer

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 +

freckles · Answer

ok cool stuff

wampominater · Answer

thanks for the help! :)