计算1/2+1/6+1/12+1/20+1/30+1/42+.2010*2011/1
问题描述：
计算1/2+1/6+1/12+1/20+1/30+1/42+.2010*2011/1
答
1-1/2+1/2-1/3+1/3-1/4+。。。。。。+1/2009-1/2010+1/2010-1/2011=1-1/2011=2010/2011
答
1/2+1/6+1/12+1/20+1/30+1/42+...1/2010*2011
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+...1/2010*2011
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+...+1/2010-1/2011
=2010/2011
答
=1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+……后面的不知道你写的什么
答
1/2=1/1*2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
根据这个运算得2010/2011
答
原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+.+1/2010-1/2011
=1-1/2011
=2010/2011