define-x-0-k-n-x-n-x-without-symbol-

Question Number 93764 by DuDono last updated on 14/May/20

define

\underset{x = 0}{\sum^{k}} \frac{n!}{x! (n - x)!}

without Σ symbol

Commented by mr W last updated on 14/May/20

d o y o u m e a n \underset{x = 0}{\sum^{n}} \frac{n!}{x! (n - x)!} ?

\underset{x = 0}{\sum^{n}} \frac{n!}{x! (n - x)!} = \underset{x = 0}{\sum^{n}} C_{x}^{n} = {(1 + 1)}^{n} = 2^{n}

Commented by DuDono last updated on 14/May/20

no, x must appear somewhere . You

can imagine it as a function if you want

Commented by mr W last updated on 14/May/20

T H E N Y O U R Q U E S T I O N I S

W R O N G!

i n \underset{x = 0}{\sum^{k}} a_{x} t h e s y m b o l x i s j u s t a c o u n t e r,

y o u c a n r e p l a c e i t w i t h a n y s y m b o l .

\underset{x = 0}{\sum^{k}} a_{x} = \underset{y = 0}{\sum^{k}} a_{y} = \underset{ψ = 0}{\sum^{k}} a_{ψ} .

\underset{x = 0}{\sum^{k}} \frac{n!}{x! (n - x)!} c a n b e a f u n c t i o n o f n

o r a f u n c t i o n o f k, b u t n e v e r a

f u n c t i o n o f x . t h i s i s s u c h b a s i c i n

m a t h e m a t i c s a s 1 + 1 = 2 .

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