Someone please help? i'm stuck this is how far i got.
1*3 + 2*4 + 3-5 ... + (n-1)*(n+1) = (n(n-1)(2n+5)/6 )for all integers >= 2.
P(2) is true since (2-1)x(2+1) = (2(2-1)(2(2)+5)/6)
3 = 3
thus P(2) is true.
Inductive step (R)
Assume P(n) is true for some n E N.
Prove that (n) x (n+2) = [(n+1)(n)(2n+1 +5)/6] is true. <-- is this correct? it looks wierd for some reason.
(n-1)x(n+1) + n x (n+2) = (n(n-1)(2n+5)/6 ) + n(n+2)
= ((n(n-1)(2n+5) + 6[n(n+2)]/6)
and this is where i got stuck. i durno how to simplify the equation could someone please tell me how to solve this problem?
Just to confirm:
could you please explain why the k from where i indicated was taken out? in the next line, and to make sure the 6 came from the fraction side rite? so it be something like 6(k+2)/6 ? wouldn't it? if possible could you show the working out how you got to the next line? because i don't really fully understand it.
sorry i'm not really good with these types of question.