1/1*3+1/3*5+1/5*7+.+1/49*51怎么算啊?

1/1×3+1/3×5＋1/5×7+…＋1/49×51 =1/2×[1-1/3]+1/2×[1/3-1/5]+1/2×[1/5-1/7]+。。。+1/2×[1/49-1/51] =1/2×[1-1/3+1/3-1/5+1/5-1/7+。+1/49-1/51] =1/2×[1-1/51] =1/2×50/51 =25/51