1+1/2-1=1/2 1/3+1/4-1/2=1/12.1/5+1/6-1/3=1/30.1/2013+1/2014-?=1/2013*2014

(1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/99)*(1-1/100)= 1/2+1/3+1/4=? 1/2-3/1-4/1= （1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/1999-1/2000)= (1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*(1+1/4)*(1-1/4)*(1+1/5)*(1-1/5)=? 1+(1/1+2)+(1/1+2+3)+(1/1+2+3+4)+(1/1+2+3+4+...+100)=? 巧算：(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4+1/5+1/6)-(1+1/2+1/3+1/4+1/5+1/6)*(1/2+1/3+1/4+1/5)(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4+1/5+1/6)-(1+1/2+1/3+1/4+1/5+1/6)*(1/2+1/3+1/4+1/5)===== 1/1*2+1/2*3+1/3*4+...+1/2000*1/2001=1/1*2+1/2*3+1/3*4+...+1/2000*1/20001= 1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+.99)= ｜1/2-1｜+｜1/3-1/2｜+1/4-1/3｜+...｜1/2009-1/2008｜+｜1/2010-1/2009｜=? (1+1/2)(1+1/3)(1+1/4)...(1+1/2009)= (1-1/2)乘(1-1/3)乘(1-1/4).乘(1-1/2000)=? 1-1/2+1/3-1/4+1/5-1/6+1/7.-1/50=? 2007*(1-1/2)*(1-1/3)*(1-1/4).(1-1/2007)=? 200×(1-1/2)×(1-1/3)×(1-1/4)×……×(1-1/100)=? 1-1/2+1/3-1/4+1/5-1/6+…+1/15=23*[1/( )+1/( )+1/( )+1/( )] (1+1/2+1/3+1/4)×(1/2+1+1/3+1/4+1/5)×(1/2+1/3+1/4) =简便方法 (1/2+1/3+1/4+.+1/2004)(1+1/2+.+1/2003)-(1+1/2+.+1/2004)(1/2+1/3+.+1/2003)=?