因为1/n(n+2)=[1/n-1/(n+2)]/2
所以
1/2*4+1/4*6+1/6*8+.+1/98*100
=1/2*(1/2-1/4)+1/2*(1/4-1/6)+1/2*(1/6-1/8)+...+1/2*(1/98-1/100)
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+...+1/98-1/100)
=1/2*(1/2-1/100)
=49/200.
因为1/n(n+2)=[1/n-1/(n+2)]/2
所以
1/2*4+1/4*6+1/6*8+.+1/98*100
=1/2*(1/2-1/4)+1/2*(1/4-1/6)+1/2*(1/6-1/8)+...+1/2*(1/98-1/100)
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+...+1/98-1/100)
=1/2*(1/2-1/100)
=49/200.