若a,b满足√a-1+√b-2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+(a+3)(b+3)……1/(a+2013)(b+2013)的值

问题描述:

若a,b满足√a-1+√b-2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+(a+3)(b+3)……1/(a+2013)(b+2013)的值

若a,b满足√a-1+√b-2=0,
则 a-1=0,b-2=0
a=1,b=2
所以
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+(a+3)(b+3)……1/(a+2013)(b+2013)
=1/1×2+1/2×3+1/3×4+.+1/2014×2015
=1-1/2+1/2-1/3+1/3-1/4+.+1/2014-1/2015
=1-1/2015
=2014/2015倒数第三步是×2015吗?是的分母是2014×2015.