已知/a-1/+/b-2/=0,试求1/ab+1/(a+1)(b+1)1/(a+2)(b+2)+...+1/(a+2010)(b+2010)的值

问题描述:

已知/a-1/+/b-2/=0,试求1/ab+1/(a+1)(b+1)1/(a+2)(b+2)+...+1/(a+2010)(b+2010)的值

1/ab+1/(a+1)(b+1)1/(a+2)(b+2)+...+1/(a+2010)(b+2010)?应该是:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2010)(b+2010)吧/a-1/+/b-2/=0 可得a=1...b=2 b-a=11/(a+n)(b+n)=1/(a+n)-1/(b+n) b+n=a+n+1所以原式=1...