规定※为：x※y=1/xy+1/(x+1)(y+A).已知2※1=1/2×1+1/(2+1)(1+A)=2/3,求25※26的值

题目

规定※为：x※y=1/xy+1/(x+1)(y+A).已知2※1=1/2×1+1/(2+1)(1+A)=2/3,求25※26的值

答案

1/2×1+1/(2+1)(1+A)=2/3
1/2+1/[3(1+A)]=2/3
1/[3(1+A)]=1/6
3(1+A)=6
1+A=2
A=1
所以25※26
=1/25×26+1/26×27
=1/25-1/26+1/26-1/27
=2/675