1/[x(x-1)]+1/[x(x+1)]+…+1/[(x+9)(x+10)]=1/(x+10)
题目
1/[x(x-1)]+1/[x(x+1)]+…+1/[(x+9)(x+10)]=1/(x+10)
答案
1/[x(x-1)]= 1/(X-1) - 1/X
1/[x(x+1)]=1/X -1/(X+1)
1/(X-1)-1/X+1/X-1/(X+1)+...+1/(X+9)-1/(X+10)
=1/(x+10)
1/(X-1)-1/(X+10)=1/(x+10)
1/(X-1)=2/(x+10)
2(x-1)=x+10
2x-2=x+10
x=12
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