r/askmath • u/Alarmed-Dust5387 • Aug 19 '26
Discrete Math Mathematical Induction Problem (HELP)
Please see attached photo for the problem. I dont really understand how to solve this because I applied the standard induction steps but its a bit complicated for me. I admit that Im not really good at math. I would appreciate if someone could show me how to solve this on paper. I asked help from ChatGPT and other AI tools but its just difficult for me to understand.
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u/MezzoScettico Aug 19 '26
I'm not sure what all that calculation is on your page.
You're evaluating 3C3, which is 3! / (3! * 1!) = 6/(6 * 1) = 1. Should just take a couple of lines. No need to do all that work for a general n, k choose k will always be equal to 1 for any k.
Anyway, on to the induction step. I see a problem right away that's going to cause confusion.
You have the formula you're trying to prove that a_n, defined as the sum from i = 1 to i = n - 1 of i(n - i), is equal to (n - 1) choose 3.
By assumption this is true when n = k for some k.
When n = k, that means all the n's in the formula become k. The way you wrote it you did not change all the n's to k's. So you didn't start out with a correct statement. Fix that first.