1/(2*4)+1/(4*6)+1/(6*8)+.+1/(48*50)
=1/2*[2/(2*4)+2/(4*6)+2/(6*8)+.+2/(48*50)
=1/2*[(4-2)/(2*4)+(6-4)/(4*6)+(8-6)/(6*8)+.+1/(48*50)
=1/2*[1/2-1/4+1/4-1/6+1/6-1/8+.+1/48-1/50]
=1/2[1/2-1/50]
=1/2*12/25
=6/25