Question

一道初一难题（1-1/2-1/3-1/4-…-1/2009)X(1/2+1/3+1/4+…+1/2010)-(1-1/2

Answer 1

设X=1-1/2-1/3-1/4-…-1/2009，Y=1/2+1/3+1/4+…+1/2009,则原式=X*(Y+1/2010)-(X-1/2010)*Y，化简后=X/2010+Y/2010=(X+Y)/2010，X+Y=1,所以原式=1/2010