Question

观察下列各式

-1×1/2=-1+1/2
-1/2×1/3=-1/2+1/3
-1/3×1/4=-1/3+1/4
......
你发现的规律是-1/n（n+1)=
用规律计算（-1×1/2）+（-1/2×1/3）+（-1/3×1/4）+......+（-1/2011×1/2012）
跪求啊。

Answer 1

-1/[n(n+1)]=-1/n+1/(n+1);

（-1×1/2）+（-1/2×1/3）+（-1/3×1/4）+......+（-1/2011×1/2012）
=-1+1/2-1/2+1/3-1/3+1/4-1/4+...+1/2011-1/2011+1/2012
=-1+1/2012
=-2011/2012

Answer 2

(-1/n)×(1/(n+1))=-1/n+1/(n+1)

（-1×1/2）+（-1/2×1/3）+（-1/3×1/4）+......+（-1/2011×1/2012）
=-1+1/2-1/2+1/3-1/3+1/4-..........-1/2011+1/2012
=-1+1/2012=-2011/2012