如何算这个阶乘的求和∑
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解决时间 2021-02-24 22:16
- 提问者网友：暗中人
- 2021-02-24 14:19
如何算这个阶乘的求和∑
最佳答案
- 五星知识达人网友：千夜
- 2021-02-24 15:03
∑(i:1->81) (160-i)!/(81-i)!
=∑(i:1->81) (160-i)(159-i)...(82-i)
=∑(i:1->81) (82-i)(83-i)....(160-i)
=(1/80) ∑(i:1->81) [ (82-i)(83-i)....(160-i)(161-i) - (81-i)(82-i)(83-i)....(160-i) ]
=(1/80) [ (82-1)(83-1)....(160-1)(161-1) - (81-81)(82-81)(83-81)....(160-81) ]
=(1/80) (81)(82)....(160)
=(1/80) [160!/80!]
=∑(i:1->81) (160-i)(159-i)...(82-i)
=∑(i:1->81) (82-i)(83-i)....(160-i)
=(1/80) ∑(i:1->81) [ (82-i)(83-i)....(160-i)(161-i) - (81-i)(82-i)(83-i)....(160-i) ]
=(1/80) [ (82-1)(83-1)....(160-1)(161-1) - (81-81)(82-81)(83-81)....(160-81) ]
=(1/80) (81)(82)....(160)
=(1/80) [160!/80!]
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