计算1/(2*4)+1/(4*6)+1/(6*8)+...+1/(98*100).
问题描述：
计算1/(2*4)+1/(4*6)+1/(6*8)+...+1/(98*100).
答
1/(2*4)
=(1/2-1/4)/2
1/(4*6)
=(1/4-1/6)/2
.
1/(98*100)
=(1/98-1/100)/2
1/(2*4)+1/(4*6)+1/(6*8)+...+1/(98*100)
=1/2(1/2-1/4+1/4-1/6.+1/98-1/100)
=1/2*(1/2-1/100)
=1/2*49/100
=49/200