找规律计算(1)(2)(3)(4)

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找规律计算(1)(2)(3)(4)

找规律计算(1)(2)(3)(4)
找规律计算(1)(2)(3)(4)
 

 

找规律计算(1)(2)(3)(4)
(1)=2(1-1/2+1/2-1/3+1/3-1/4……+1/99-1/100)
=1(1-1/100)=50/99
(2)1/2(1/3-1/5+1/5-1/7+……+1/21-1/23)
=1/2(1/3-1/23)
=5/48
(3)=1/3+1/4-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)-(1/8+1/9)
=1/3-1/9
=2/9
(4)(3/2)×(5/4)×(7/6)……×(11/10)×(2/3)×(4/5)×……×(8/9)
=[(3/2)×(2/3)][(5/4)×(4/5)]×……×[(9/8)×(8/9)]×(11/10)
=11/10