裂项相消,1/1*2+1/2*3..+1/19*20 写出过程
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![裂项相消,1/1*2+1/2*3..+1/19*20 写出过程](/uploads/image/z/14542210-10-0.jpg?t=%E8%A3%82%E9%A1%B9%E7%9B%B8%E6%B6%88%2C1%2F1%2A2%2B1%2F2%2A3..%2B1%2F19%2A20+%E5%86%99%E5%87%BA%E8%BF%87%E7%A8%8B)
裂项相消,1/1*2+1/2*3..+1/19*20 写出过程
裂项相消,1/1*2+1/2*3..+1/19*20 写出过程
裂项相消,1/1*2+1/2*3..+1/19*20 写出过程
1/1*2+1/2*3..+1/19*20
=1-1/2+1/2-1/3+1/3-1/4+……+1/19-1/20
=1-1/20
=19/20
1/1*2+1/2*3.。。。。。+1/19*20
=(1/1 - 1/2) + (1/2-1/3) + (1/3-1/4) + ...... + (1/19 - 1/20)
=1-1/20
=19/20
1/n-1/n+1=1/n(n+1),可以验证下