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=1×2×3×4×5×……×n[x/1!]+[x/2!]+[x/3!]+[x/4!]+……+[x/2006!]=226求x?(其中“/”为分号)最好有过程.
题目详情
=1×2×3×4×5×……×n
[x/1!]+[x/2!]+[x/3!]+[x/4!]+……+[x/2006!]=226
求x?
(其中“/”为分号)
最好有过程.
[x/1!]+[x/2!]+[x/3!]+[x/4!]+……+[x/2006!]=226
求x?
(其中“/”为分号)
最好有过程.
▼优质解答
答案和解析
1/(1*2*3*4)+1/(2*3*4*5)+.+1/[n*(n+1)*(n+2)*(n+3)]
=1/3{1/(1*2*3)-1/(2*3*4)+1/(2*3*4)-1/(3*4*5)+.+1/[n*(n+1)*(n+2)]-1/[(n+1)*(n+2)*(n+3)]}
=1/3{1/6-1/[(n+1)*(n+2)*(n+3)]}
=1/3*6-1/[3(n+1)*(n+2)*(n+3)]
1/18-1/[3(n+1)*(n+2)*(n+3)]
=1/3{1/(1*2*3)-1/(2*3*4)+1/(2*3*4)-1/(3*4*5)+.+1/[n*(n+1)*(n+2)]-1/[(n+1)*(n+2)*(n+3)]}
=1/3{1/6-1/[(n+1)*(n+2)*(n+3)]}
=1/3*6-1/[3(n+1)*(n+2)*(n+3)]
1/18-1/[3(n+1)*(n+2)*(n+3)]
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