Prove that :
5C5 + 6C5 + 7C5 + 8C5 + ........ + (n - 2)C5 + (n - 1)C5 = nC6
[Remark: If ever possible, don't use MI to prove, points will be given to those not using MI if there is a choice.]
Combination
2010-10-01 2:18 am
回答 (1)
2010-10-01 2:31 am
✔ 最佳答案
The important formula : nCm = (n+1)C(m+1) - nC(m+1) is used :5C5 + (6C5) + (7C5) + (8C5) + ........ + (n - 2)C5 + (n - 1)C5 = 5C5 + (7C6 - 6C6) + (8C6 - 7C6) + (9C6 - 8C6) + ... + [(n-1)C6 - (n-2)C6]+ [nC6 - (n-1)C6]= 5C5 - 6C6 + nC6= nC6
收錄日期: 2021-04-21 22:15:53
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