1/2+1/6+1/12+1/20+1/30+1/42+.+1/2010*2011+1/2011*2012等于多少?

问题描述:

1/2+1/6+1/12+1/20+1/30+1/42+.+1/2010*2011+1/2011*2012等于多少?

1×1/2+1/2×1/3+1/3×1/4+1/4×1/5+.1/2010×1/2011+1/2011×1/2012
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/2010-1/2011+1/2011-1/2012
=1-1/2012
=2011/2012