1/2*4+1/4*6+1/6*8+1/8*10+...+1/98*100
=1/2(1/2-1/4)+1/2(1/4-1/6)+...+1/2(1/98-1/100)
=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
1/2*4+1/4*6+1/6*8+1/8*10+...+1/98*100
=1/2(1/2-1/4)+1/2(1/4-1/6)+...+1/2(1/98-1/100)
=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