15题.定义一种运算“^”:x^y=1/xy+1/(X+1)+1/(Y+1),求2007^2008的值.

问题描述:

15题.定义一种运算“^”:x^y=1/xy+1/(X+1)+1/(Y+1),求2007^2008的值.

1|2007乘2008|(2007+1)+1|2008+1

2007^2008=1/(2007×2008)+1/(2007+1)+1/(2008+1)
=1/2007-1/2008+1/2008+1/2009
=1/2007+1/2009
=(2007+2009)/(2007×2009)
=4016/4032063