问题标题:
1/[x(x-1)]+1/[x(x+1)]+…+1/[(x+9)(x+10)]=1/(x+10)
问题描述:

1/[x(x-1)]+1/[x(x+1)]+…+1/[(x+9)(x+10)]=1/(x+10)

吕春芬回答:
  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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