1+(1/(1+(1/(1+(1/(1+2008))))))=
1+(1/(1+(1/(1+(1/(1+2008))))))=
<gadget id="calculator">1 + 2_008</gadget>
<output>2_009</output>

<gadget id="calculator">1 / 2_009</gadget>
<output>1/2_009 = around 0.000498</output>

<gadget id="calculator">1 + (1/2_009)</gadget>
<output>2_010/2_009 = around 1.000498</output>

<gadget id="calculator">1 / (2_010/2_009)</gadget>
<output>2_009/2_010 = around 0.999502</output>

<gadget id="calculator">1 + (2_009/2_010)</gadget>
<output>4_019/2_010 = around 1.999502</output>

<gadget id="calculator">1 / (4_019/2_010)</gadget>
<output>2_010/4_019 = around 0.500124</output>

<gadget id="calculator">1 + (2_010/4_019)</gadget>
<output>6_029/4_019 = around 1.500124</output>

<result>6_029/4_019 = around 1.500124</result>