一道高中数学题

2am/(am+2)=2-4/(am+2) 原式=2m-4?【（1/(a?+2)+1/(a?+2)+1/(a?+2)+...+1/(am+2）】 a?=2 a?=4 a?=12 a?=84 1/(a?+2)+1/(a?+2)+1/(a?+2)+...+1/(am+2)=1/4+1/6+1/18+1/84....=0.25+0.16667+0.05556+0.01190+....(a?+2)+1/(a?+2)+1/(a?+2)+...+1/(am+2）】=0 又 1/(a?+2)+1/(a?+2)+1/(a?+2)+...+1/(am+2)>1/22+1/23+1/2?+....=1/22?(1-1/2^(m-2))/(1-1/2)=1/2?(1-1/2^(m-2))<0.5 得【（1/(a?+2)+1/(a?+2)+1/(a?+2)+...+1/(am+2）】=0 故 原式=2m=2016 m=1008 选A

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