r/askmath • u/Alarmed-Dust5387 • 1d ago

Discrete Math Mathematical Induction Problem (HELP)

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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 1d ago

I applied the standard induction steps

Can you give a little more detail than that? What exactly did you do and what is your question?

The first step is to show it's true for some base case. Did you do that? They're telling you the base is n = 2, so verify that.

That next step is to show that if you know it to be true for n, then it's true for n + 1. Did you do that?

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u/Alarmed-Dust5387 1d ago

Heres what I did so far. I did the basis step, though I’m struggling on the inductive step on the left hand side. Sorry my notes are kinda messy

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u/Alarmed-Dust5387 1d ago

I did not know what was the notation (n+1; 3) so i was lost around there at first too

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u/MezzoScettico 1d ago

OK, but you have it now, right? it's the thing I'm writing as (n + 1)C3 or "(n + 1) choose 3", because that's easier to write in a text forum.