Bingk
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Prove that
[itex]R(p,q) \leq \left(\stackrel{p+q-2}{p-1}\right)[/itex]
where [itex]p[/itex] and [itex]q[/itex] are positive integers
I'm supposed to use induction on the inequality [itex]R(p,q) \leq R(p-1,q) + R(p,q-1)[/itex], but I'm having difficulty there.
How do I go about doing this? I can show it's true for [itex]p=q=1[/itex].
But, I can't see how I get the combination in the first inequality from an induction on the second inequality (which doesn't contain a combination) ...
[itex]R(p,q) \leq \left(\stackrel{p+q-2}{p-1}\right)[/itex]
where [itex]p[/itex] and [itex]q[/itex] are positive integers
I'm supposed to use induction on the inequality [itex]R(p,q) \leq R(p-1,q) + R(p,q-1)[/itex], but I'm having difficulty there.
How do I go about doing this? I can show it's true for [itex]p=q=1[/itex].
But, I can't see how I get the combination in the first inequality from an induction on the second inequality (which doesn't contain a combination) ...