如果有理数ab满足ab-2的绝对值+1-b的绝对值=0,试求:ab/1 + (a+1)(b+1)/1 + (a+2)(b+2)/1 +.如果有理数ab满足ab-2的绝对值+1-b的绝对值=0,试求:ab/1 + (a+1)(b+1)/1 + (a+2)(b+2)/1 +.(a+2003)(b+2003)/1 的值.注:
问题描述:
如果有理数ab满足ab-2的绝对值+1-b的绝对值=0,试求:ab/1 + (a+1)(b+1)/1 + (a+2)(b+2)/1 +.
如果有理数ab满足ab-2的绝对值+1-b的绝对值=0,试求:
ab/1 + (a+1)(b+1)/1 + (a+2)(b+2)/1 +.(a+2003)(b+2003)/1 的值.
注:
答
∵|ab-2|+|1-b|=0 ∴ab-2=0,1-b=0∴ab=2,b=1∴a=2,b=1 1/ab + 1/(a+1)(b+1) + 1/(a+2)(b+2)+.1/(a+2003)(b+2003)=1/1×2+1/3×2 +1/4×3+……..+1/2005×2004=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2004-1/200...