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I'm having trouble with a math induction problem. I've been doing other proofs (summations of the integers etc) but I just can't seem to get my head around this.

Q. Prove using induction that $n^2 \leq n!$

So, assume that $P(k)$ is true: $k^2 \leq k!$

Prove that $P(k+1)$ is true: $(k+1)^2 \leq (k+1)!$

I know that $(k+1)! = (k+1)k!$ so: $(k+1)^2 \leq (k+1)k!$ but where can I go from here?

Any help would be much appreciated.

  • 5
    Hint: it isn't true.2012-10-29

3 Answers 3