1/1X2+1/2X3+1/3X4+……1/2003X2004用拆項法解决

1/1X2+1/2X3+1/3X4+……1/2003X2004用拆項法解决


1/1X2+1/2X3+1/3X4+……1/2003X2004
=1-1/2+1/2-1/3+1/3-1/4+…+1/2003-1/2004
=1-1/2004
=2003/2004



3/(1x2)+3/(2x3)+3/(3x4)+.+3/(2003x2004)=?


原式=3(1/1*1/2+1/2*1/3+……+1/2003*1/2004)=3[(1/1-1/2)+(1/2-1/3)+……+(1/2003-1/2004)]=2(1-1/2004)=6009/2004



(1/2006-1)(1/2005-1)(1/2004-1)…(1/1000-1)
寫出過程,講解!急!~~


=(-2005/2006)(-2004/2005)……(-999/1000)
=-999/2006