Rising Factorial (Problem $1$ )

Algebra Level 2

$100^{(4)} =$

Hint: $x^{(n)}$ denotes the rising factorial

For more information about rising and falling factorials, check out the Wikipedia article .

2 solutions

A Former Brilliant Member
Jul 14, 2020

By definition, for positive integers $m$ and $n$ ,

$m^{(n) }=\dfrac {(m+n-1)!}{(m-1)!}$

So $100^{(4)}=\dfrac {103!}{99!}=\boxed {106110600}$ .

Nice! You know that mine is simpler, though, by using $x^{(4)}$ and substituting $x = 100$ ? @Alak Bhattacharya

Yajat Shamji - 11 months ago

For this particular problem only. How will you do with $100^{(50)}$ , or to be worse, $999^{(199)}$ ?

A Former Brilliant Member - 11 months ago

You can't do anything over $x^{(7)}$ when $x \geq 100$ .

Yajat Shamji - 11 months ago

@Yajat Shamji – Why? Does the definition break down for those values?!!

A Former Brilliant Member - 11 months ago

@A Former Brilliant Member – No calculator can calculate beyond it. For the human mind, this may as well be the limit.

Yajat Shamji - 11 months ago

Yajat Shamji
Jul 14, 2020

$100^{(4)} = 100(101)(102)(103) = \fbox{106110600}$