已知|ab‐8|+|2‐a|=0求1∕ab+1∕(a+2)(b﹢2)﹢1∕(a﹢4)(b+4)+.+1∕(a+2012)(b+2012)的值

Question

已知|ab‐8|+|2‐a|=0 求1∕ab+1∕(a+2)(b﹢2)﹢1∕(a﹢4)(b+4)+.+1∕(a+2012)(b+2012)的值

Answer 1

由a-2=0 ab-8=0
解得a=2 b=4
所以1/ab+1/(a+1)(b+1)+1/(a+2)(b+2).+1/（a+2012）（b+2012）
=1/2[1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2013×2014)]
=1/2[(1-1/2)+(1/2-1/3)+……+(1/2013-1/2014)]
=1/2(1-1/2014)
=4026/4028
不明白再问,