问题标题：
【初二数学观察下列各式：1/2=1/1*2=1/1-1/2,1/6=1/2*3=1/2-1/3,1/12=1/3*4=1/3-1/4,1/20=1/4*5=1/4-1/5...1)请利用上述规律计算:1/2+1/6+1/12+...+1/(n-1)n+1/n(n+1)2)请利用上述规律,解方程:1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x】
问题描述：
初二数学
观察下列各式：1/2=1/1*2=1/1-1/2,1/6=1/2*3=1/2-1/3,1/12=1/3*4=1/3-1/4,1/20=1/4*5=1/4-1/5
...
1)请利用上述规律计算:
1/2+1/6+1/12+...+1/(n-1)n+1/n(n+1)
2)请利用上述规律,解方程:
1/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)=1/x+1
石振锋回答：
1/2+1/6+1/12+...+1/(n-1)n+1/n(n+1)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/n-1-1/n)+(1/n-1/n+1)=1-1/n+11/(x-4)(x-3)+1/(x-3)(x-2)+1/(x-2)(x-1)+1/(x-1)x+1/x(x+1)=1/x+1=1/(x-4)-1/(x-3)+1/(x-3)-1/(x-2)+1/(x-2...
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