Induction Proof Help

Question

Q: By induction on n prove that for all positive integers $n^2\ge1$

A: When n=1, $$n^2\ge1=1^2\ge1$$$$1\ge1$$

Suppose n=k, $$n^2\ge1=k^2\ge1$$

** This is as far as I can get unto without getting stuck, I know that I have to assume that n=k+1 for the last part, but it is what I do after that. Any help would be appreciated.

you can use that $\forall n>0, (n+1)^2>n^2$ – NHL Jan 05 '21 at 11:46 — NHL, Jan 05 '21 at 11:46

score 1 · Accepted Answer · answered Jan 05 '21 at 11:53

1

If $n^2\geqslant1$, then$$(n+1)^2=n^2+2n+1\geqslant1+2n+1\geqslant1..$$

answered Jan 05 '21 at 11:53

José Carlos Santos

427,504

Induction Proof Help

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