For a natural number x, f(x)=(1/(1+x)), such as f4=(1/(1+4))=(1/5), f((1/4))=(1 /(1+(1/4)))=(4/5), then f2012+f2011+…+f2+f1+f((1/2))+…f((1/2011))+f(( 1/2012)) = how much.
对于自然数x，规定f(x)=(1/(1+x))，例如f4=(1/(1+4))=(1/5)，f((1/4))=(1/(1+(1/4)))=(4/5)，则f2012+f2011+…+f2+f1+f((1/2))+…f((1/2011))+f((1/2012))=多少．
<gadget id="calculator">1 + 1</gadget>
<output>2</output>

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">2_011 + (1/2)</gadget>
<output>4_023/2 = around 2_011.5</output>

<result>4_023/2 = around 2_011.5</result>