Question

一道改编的高中数学题

做了一下，总感觉奇奇怪怪，感觉这题目似乎出错了，帮忙看一下啦？
12题哈

Answer 1

2am/(am+2)=2-4/(am+2)
原式=2m-4•【（1/(a₁+2)+1/(a₂+2)+1/(a₃+2)+...+1/(am+2）】
a₁=2
a₂=4
a₃=12
a₄=84
1/(a₁+2)+1/(a₂+2)+1/(a₃+2)+...+1/(am+2)=1/4+1/6+1/18+1/84....=0.25+0.16667+0.05556+0.01190+....<0.5
则 【（1/(a₁+2)+1/(a₂+2)+1/(a₃+2)+...+1/(am+2）】=0
又 1/(a₁+2)+1/(a₂+2)+1/(a₃+2)+...+1/(am+2)>1/2²+1/2³+1/2⁴+....=1/2²•(1-1/2^(m-2))/(1-1/2)=1/2•(1-1/2^(m-2))<0.5
得【（1/(a₁+2)+1/(a₂+2)+1/(a₃+2)+...+1/(am+2）】=0
故 原式=2m=2016
m=1008
选A