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In this session, they were discussing the meaning of combinatorial notation and discussing the addition rule of Pascal's Identity in terms of that notation. They were asked to write the general form of Pascal's Identity starting from discussing the coefficients of the expansion of (a+b)^n. ...
0≤k≤a+b, 总共可能的情况为:从A拿0个B拿k个 + 从A拿1个B拿k−1个 + 从A拿2个B拿k−2个 + ... +从A拿k−1个B拿1个 + 从A拿k个B拿0个,化简就是(a+bk)=Σs=0k(as)(bk−s),这个也叫Chu-Vandermount formula或者Committee selection identity....
[The hockey-stick identity]Look at the column indexed by r = 2 in Pascal's triangle:2C2+3C2+C2+3C2+C2=1+3+6+10+15=35=C3.(*)The general form of this well-known hockey-stick identity is C,++C,++2C,++"C,="+Cr+(**)where n and r are whole numbers with 0 ≤ r s n....
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要从这两堆球里面拿共计k个球,0≤k≤a+b, 总共可能的情况为:从A拿0个B拿k个 + 从A拿1个B拿k−1个 + 从A拿2个B拿k−2个 + ... +从A拿k−1个B拿1个 + 从A拿k个B拿0个,化简就是(a+bk)=Σs=0k(as)(bk−s),这个也叫Chu-Vandermount formula或者Committee selection identity....
For more information, see the developer’s privacy policy. Data Used to Track You The following data may be used to track you across apps and websites owned by other companies: Identifiers Data Not Linked to You The following data may be collected but it is not linked to your identity...