What-is-5-

Question Number 217873 by ahmed2025 last updated on 22/Mar/25

W h a t i s 5^{!} = ?

Commented by mr W last updated on 23/Mar/25

i {d o n}^{'} t t h i n k 5^{!} i s a c o m m o n v a l i d

m a t h e m a t i c a l n o t a t i o n, w h i l e 5!,

5!! a n d! 5 a r e .

p l e a s e s h o w w h e r e y o u s e e i t a n d

i n w h i c h c o n t e x t .

Answered by MrGaster last updated on 23/Mar/25

! 5 = 5! \underset{k = 0}{\sum^{5}} \frac{{(- 1)}^{k}}{k!}

5! = 120

\underset{k = 0}{\sum^{5}} \frac{{(- 1)}^{k}}{k!} = 1 - 1 + \frac{1}{2} - \frac{1}{6} + \frac{1}{24} - \frac{1}{120} = \frac{44}{120}

5! = 120 \times \frac{44}{120} = 44

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