计算ab/(a+b-1)(a+b)+ab/(a+b)(a+b+1)+ab/(a+b+1)(a+b+2)+.+ab/(a+b+98)(a+b+99)+ab/(a+b+99)(a+b+100)
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![计算ab/(a+b-1)(a+b)+ab/(a+b)(a+b+1)+ab/(a+b+1)(a+b+2)+.+ab/(a+b+98)(a+b+99)+ab/(a+b+99)(a+b+100)](/uploads/image/z/2985019-43-9.jpg?t=%E8%AE%A1%E7%AE%97ab%2F%28a%2Bb-1%29%28a%2Bb%29%2Bab%2F%28a%2Bb%29%28a%2Bb%2B1%29%2Bab%2F%28a%2Bb%2B1%29%28a%2Bb%2B2%29%2B.%2Bab%2F%28a%2Bb%2B98%29%28a%2Bb%2B99%29%2Bab%2F%28a%2Bb%2B99%29%28a%2Bb%2B100%29)
计算ab/(a+b-1)(a+b)+ab/(a+b)(a+b+1)+ab/(a+b+1)(a+b+2)+.+ab/(a+b+98)(a+b+99)+ab/(a+b+99)(a+b+100)
计算ab/(a+b-1)(a+b)+ab/(a+b)(a+b+1)+ab/(a+b+1)(a+b+2)+.+ab/(a+b+98)(a+b+99)+ab/(a+b+99)(a+b+100)
计算ab/(a+b-1)(a+b)+ab/(a+b)(a+b+1)+ab/(a+b+1)(a+b+2)+.+ab/(a+b+98)(a+b+99)+ab/(a+b+99)(a+b+100)
ab/(a+b-1)(a+b)+ab/(a+b)(a+b+1)+ab/(a+b+1)(a+b+2)+.+ab/(a+b+98)(a+b+99)+ab/(a+b+99)(a+b+100)
=ab[1/(a+b-1)-1/(a+b)+1/(a+b)-1/(a+b+1)+.+1/(a+b+98)-1/(a+b+99)+1/(a+b+99)-1/(a+b+100)]
=ab*[1/(a+b-1)-1/(a+b+100)]
=ab(a+b+100-a-b+1)/[(a+b-1)(a+b+100)]
=101ab/[(a+b-1)(a+b+100)]
此题需要用到1/(n-1)n=1/(n-1)-1/n,记住这个式子很多题都可以用到的。
原式=ab×[1/(a+b-1)(a+b)+1/(a+b)(a+b+1)+1/(a+b+1)(a+b+2)+....+1/(a+b+98)(a+b+99)+1/(a+b+99)(a+b+100)]=ab×[1/(a+b-1)-1/(a+b)+1/(a+b)-1/(a+b+1)+1/(a+b+1)-1/(...
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此题需要用到1/(n-1)n=1/(n-1)-1/n,记住这个式子很多题都可以用到的。
原式=ab×[1/(a+b-1)(a+b)+1/(a+b)(a+b+1)+1/(a+b+1)(a+b+2)+....+1/(a+b+98)(a+b+99)+1/(a+b+99)(a+b+100)]=ab×[1/(a+b-1)-1/(a+b)+1/(a+b)-1/(a+b+1)+1/(a+b+1)-1/(a+b+2)+....+1/(a+b+98)-1/(a+b+99)+1/(a+b+99)-1/(a+b+100)]=ab×[1/(a+b-1)-1/(a+b+100)]=101ab
/(a+b-1)(a+b+100)
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