1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+2007)

问题描述:

1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+2007)

1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+2007)=2/1*2 +2/2*3 +2/3*4 +2/4*5 +……+2/2007*2008=2*(1/1-1/2 +1/2 -1/3+1/3-1/4+1/4-1/5+……+1/2007-1/2008)=2*(1-1/2008)=4014/2008=2007/1004...