Verify that is true & assume valid your proposition for Hence, we must prove that
Observe that,
which is after simplification, the result we wanted to prove.
prove that sigma(1/r(r+1)(r+2)=0.25-1/2(n+1)(n+2)
it is the proving for k+1 i have a question about, do you put both sides equal to each other and the expand/simplify one side using the fact that you have assumed it is true for k and the show that both sides equal each other. my teacher went over this recently however i belive she got it wrong, any help would be greatly appreciated.
You're proving the statement by mathematical induction. You're assuming your proposition valid for and for some The next step is to prove that for the equality does hold, which is I've done above.
If you want to "rearrange" to get you'll need no induction, but telescoping series will be helpful.