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Rapid Increase
What comes next in this series?
0, 1, 2, 720!, ?
In math, the exclamation mark is a factorial, which is the product of every whole number from 1 to n.
For example, five factorial is written 5! = 1x2x3x4x5 = 120. By definition 0! = 1.
So 720! = 1x2x3x4x...718x719x720, which is a very large number.
0, 1, 2, 720!, ?
In math, the exclamation mark is a factorial, which is the product of every whole number from 1 to n.
For example, five factorial is written 5! = 1x2x3x4x5 = 120. By definition 0! = 1.
So 720! = 1x2x3x4x...718x719x720, which is a very large number.
Hint
Look at the first few factorials:0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
Answer
The crucial insight is that 6! = 720, so you can rewrite the series as:0, 1, 2, (6!)!, ?
Then note that 3! = 6, so you can rewrite the series again as:
0, 1, 2, ((3!)!)!, ?
You might think the series is:
0!!!, 1!!!, 2!!!, 3!!!, ...
However, 0!!! = 1, so the series must be:
0, 1!, 2!!, 3!!!, ...
Thus, the next term is 4!!!!.
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