Question 71
If $n$ and $k$ are positive integers, then $$
(n+1) \cdot(n+2) \cdot \ldots \cdot(n+k)\lt (n+k)^{k}
$$ use this to determine which of the two following numbers is greater than the other: $(100!)$ ! and $99!^{100!} \cdot 100!^{99!}$.
(n+1) \cdot(n+2) \cdot \ldots \cdot(n+k)\lt (n+k)^{k}
$$ use this to determine which of the two following numbers is greater than the other: $(100!)$ ! and $99!^{100!} \cdot 100!^{99!}$.