1⼀(2*4)+1⼀(4*6)+1⼀(6*8)+1⼀(8*10)+......+1⼀(1996*1998)等于多少

1/(2*4)+1/(4*6)+1/(6*8)+1/(8*10)+......+1/(1996*1998)
=1/2(1/2-1/4+1/4.....1/1996-1/1998)
=1/2(1/2-1/1998)
=499/1998

（1/2-1/4+1/4-1/6·····+1/1996-1/1998）/2=
（1/2-1/1998）/2=499/1988

1/n*(n+2)=1/2*[1/n-1/(n+2)]

1/(2*4)+1/(4*6)+1/(6*8)+1/(8*10)+......+1/(1996*1998)
=1/2*[1/2-1/4+1/4-1/6+....+1/1996-1/*1998]
=1/2*(1/2-1/1998)
=1/2*998/1998
=499/1998

原式可化为1/4*(1/1*2+1/2*3+1/3*4+......1/998*999)
=1/4*(1-1/2+1/2-1/3+1/3-1/4+......+1/998-1/999) 公式1/n*(n+1)=1/n-1/n+1
=1/4*(1-1/999)
=1/4*998/999
=499/1998