若n为正整数，观察下列各式：①11×3＝12(1−13)；②13×5＝12(13−15)；③15×7＝12(15−17)…根据观察计算并填空：（1）11×3+13×5+15×7=（2）11×3+13×5+15×7+…+1(2n−1)(2n+1)=．

Question

若n为正整数，观察下列各式：
①(1)/(1×3)＝(1)/(2)(1−(1)/(3))；②(1)/(3×5)＝(1)/(2)((1)/(3)−(1)/(5))；③(1)/(5×7)＝(1)/(2)((1)/(5)−(1)/(7))…
根据观察计算并填空：
（1）(1)/(1×3)+(1)/(3×5)+(1)/(5×7)=______
（2）(1)/(1×3)+(1)/(3×5)+(1)/(5×7)+…+(1)/((2n−1)(2n+1))=______．

Answer 1

（1）(1)/(1×3)+(1)/(3×5)+(1)/(5×7)=(1)/(2)（1-(1)/(3)+(1)/(3)-(1)/(5)+(1)/(5)-(1)/(7)）=(1)/(2)×(6)/(7)=(3)/(7)；
（2）原式=(1)/(2)（1-(1)/(3)+(1)/(3)-(1)/(5)+…+(1)/(2n−1)-(1)/(2n+1)）=(1)/(2)×(2n+1−1)/(2n+1)=(n)/(2n+1)．
故答案是(3)/(7)；(n)/(2n+1)．