is n! = $\theta((n+1!))$ Asymptotic notation

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I had a doubt whether n!=$\theta{(n+1)!}$.

In my opinion, it should be correct, as there must surely exist values for $c_1$, $c_2$ such that the definition for asymptotic notation is satisfied.

But my assignment solution simply says that it's not so and doesn't provide any explanation. I tried searching through the web, but to no avail.

Is my solution correct? And if not, what am I missing, which has led to the wrong answer?

Thanks in advance!