Question

能帮我解一个题目吗？谢谢！ 1/1*3+1/3*5+1/5*7+1/7*9+………+1/49*51拜托各位了 3Q

Answer 1

1/1*3=(1-1/3)/2 1/3*5=(1/3-1/5)/2 ... 1/49*51=(1/49-1/51)/2 所以： 1/1*3+1/3*5+1/5*7+1/7*9+………+1/49*51 =(1-1/3+1/3-1/5+1/5-1/7+...+1/49-1/51)/2 =(1-1/51)/2 =25/51

Answer 2

1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+……+1/(49x51) =(1/2)x[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+……+(1/49-1/51)] =(1/2)x(1-1/51) =25/51