Suppose that $n = 98!$. What is $100!$ in terms of $n$?

Question

If $n = 98!$ then how do we find $100!$ in terms of $n$?

I am really stumped on this tricky question.

Answer 1

Hint:

$k!=\underbrace{1\cdot 2\cdot 3\cdots \cdot (k-1)\cdot k}_{k~\text{terms}}$

Now, noticing that $k!=(\underbrace{1\cdot 2\cdots (k-1)}_{(k-1)~\text{terms}})\cdot k = ((k-1)!)\cdot k$ you should be able to continue.