1\2+2\2*3+3\2*3*4+4\2*3*4*5.+8\2*3*4*5*6*7*8*9=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/01 06:40:36
![1\2+2\2*3+3\2*3*4+4\2*3*4*5.+8\2*3*4*5*6*7*8*9=?](/uploads/image/z/14620-4-0.jpg?t=1%5C2%2B2%5C2%2A3%2B3%5C2%2A3%2A4%2B4%5C2%2A3%2A4%2A5.%2B8%5C2%2A3%2A4%2A5%2A6%2A7%2A8%2A9%3D%3F)
1\2+2\2*3+3\2*3*4+4\2*3*4*5.+8\2*3*4*5*6*7*8*9=?
1\2+2\2*3+3\2*3*4+4\2*3*4*5.+8\2*3*4*5*6*7*8*9=?
1\2+2\2*3+3\2*3*4+4\2*3*4*5.+8\2*3*4*5*6*7*8*9=?
1/2=1-1/2
2/2*3=1/2-1/2*3
……
n/2*3*…(n+1)=1/2*3*…*n -1/2*3*…*(n+1)
所以原式 =(1-1/2)+(1/2-1/2*3)+…+(1/2*3*…*8 -1/2*3*…*9)
=1-1/2*3*…*9=362879/362880