What have you found for these years?

2010-03-08

Proofs without words

open audio shared 的:
經典證明:1+2+3+...+ (n-1) = C(n,2)
(sorry, 字型因素,轉繁體)

mmm... interesting, but indeed it's not a proof,
just an explanation. 可惜我也沒受過寫證明的訓練,
只能簡單地把式子隨便換一下:

C(n, 2) = (n*(n-1)) / (2*1) -- formula
1+2+3+...+(n-1) = (1+(n-1)) * ((n-1) / 2) -- formula
= (1+(n-1)) * (n-1) / 2
= ((1+(n-1)) * (n-1)) / 2
= ((1+n-1) * (n-1)) / 2
= (n*(n-1)) / 2 -- formula
= C(n, 2)

依此類推,其實 C(n, 2) 可以想像成很多事

==
呃,這不是程式,不過我也不會講數學,就不額外開 tag 了...

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