(求大神解)已知Ia+1I+Iab-2I=0,求下列数字值:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2014)(b+2014)明天要上学了,改正一下是式子值

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(求大神解)已知Ia+1I+Iab-2I=0,求下列数字值:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2014)(b+2014)明天要上学了,改正一下是式子值
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(求大神解)已知Ia+1I+Iab-2I=0,求下列数字值:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2014)(b+2014)明天要上学了,改正一下是式子值
(求大神解)已知Ia+1I+Iab-2I=0,求下列数字值:
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2014)(b+2014)
明天要上学了,
改正一下是式子值

(求大神解)已知Ia+1I+Iab-2I=0,求下列数字值:1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2014)(b+2014)明天要上学了,改正一下是式子值
∵|a-1|+|ab-2|=0
∴a-1=0 ab-2=0
∴a=1 b=2
∴原式=1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2015×2016)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2015-1/2016
=1-1/2016
=2015/2016