1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+……+1/20*21*22
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/13 12:28:28
![1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+……+1/20*21*22](/uploads/image/z/133453-37-3.jpg?t=1%2F1%2A2%2A3%2B1%2F2%2A3%2A4%2B1%2F3%2A4%2A5%2B1%2F4%2A5%2A6%2B%E2%80%A6%E2%80%A6%2B1%2F20%2A21%2A22)
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1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+……+1/20*21*22
1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+……+1/20*21*22
1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+……+1/20*21*22
裂项相消 1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+……+1/20*21*22=0.5(1/1*2-1/2*3+1/2*3-1/3*4.)=0.5*(0.5-1/21*22)