问题补充说明:一直加到1加2加3……加1999
因为:
1+2=2*3/2
1+2+3=3*4/2
1+2+3+4没命=4*5/2
1+2+3+……+100=100*101/2
所以,
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+...+2006)
=1+2/(2*3)+2/(3*4)+2/(4*5)+……+2/(100*101)
=2[(来自1/2+1/(2*3)+1/(3*4)+1/(4*5)+……+1/(100*101)〕
因为:
1/(2*3)=1/2-1/3;
1/(3*4)=1/3-1/4;
1/(4*5)=1/4-1/5;
……
1/(100*101)=1/100-1/101
所以,
原式=2(360问答1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/100-1/101)
=2(1-1/101)
=2*100/101
=200/101