So I came across this induction question and am quite stuck mid-way.
The question is: Prove that is divisible by for all odd integers
So far, I have this working out done:
1. To prove: , where
Prove true for
which is divisible by 3
So the statement is true for
2. Assume true for , where
i.e. , where
3. Prove true for
To prove: , where
Aaaand I'm stuck at that step. I've no idea how to manipulate the LHS so that the assumption from 2 can be subbed into 3. Also, is the working so far correct? Thanks!
Also, thanks for posting your attempts!
Thank you for pointing that out! Even in written down working out, I keep forgetting that plus sign, so I'll make sure to check that it's in next time, haha.
In class, my teacher said that when proving for odd integers, you should always use the assumption so that the odd integer 1 is not excluded! Is that true or is still alright to use ?
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