The factorial function is defined as

*n! = 1, if n = 0*

*= n(n-1)!, if n > 0*

It is recursively defined using products.

It can also be expressed as a recursive summation

Let's see what 3! looks like

3! is simply 3 groups of 2 groups of 1

*(1 + 1) +*

*(1 + 1) +*

*(1 + 1)*

similarly 4! is 4 groups of 3 groups of 2 groups of 1 (I.e. four copies of the above)

*((1 + 1) +*

*(1 + 1) +*

*(1 + 1) ) +*

*((1 + 1) +*

*(1 + 1) +*

*(1 + 1) ) +*

*((1 + 1) +*

*(1 + 1) +*

*(1 + 1) ) +*

*((1 + 1) +*

*(1 + 1) +*

*(1 + 1) )*

Now we can visualize why factorials "grow" like crazy..(10! may take up an entire book)

*"Why bats, Master Wayne?"*

*"Bats frighten me. It's time my enemies shared my dread."*

*-From Batman Begins*

## 2 comments:

I actually did not understand what you were trying to convey!! :-?

Vivek.

Well, I've got to improve on my writing skills :). I think writing down factorials as summation helps to better visualize their fast growth rate.It's true or maybe it's just me :-).

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