答：分数的裂项知识
1/(1*3) 1/(2*4) 1/(3*5) ...1/(49*51
=(1/2)* (1-1/3+1/2-1/4+1/3-1/5+.+1/48-1/50+1/49-1/51)
=(1/2)*(1+1/2-1/50-1/51)
=(1/2)*(3/2-101/2550)
=3/4 -101/5100
=3825/5100 -101/5100
=3724 /5100