已知:字母a、b满足√(a-1)+│b-2│=0求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2008)(b+2008)的值?
问题描述:
已知:字母a、b满足√(a-1)+│b-2│=0求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2008)(b+2008)的值?
答
√(a-1)+│b-2│=0a-1=b-2=0a=1 b=21/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2008)(b+2008)=1/1*2+1/2*3+1/3*4+...+1/2009*2010=1/1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010=1-1/2010=2009/2010