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Compare (Posted on 2011-07-26) Difficulty: 4 of 5
Which is bigger: ln(1.01) or 2/201?
Pen and paper only.

No Solution Yet Submitted by Ady TZIDON    
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Solution solution | Comment 1 of 3

Use of a series to derive ln(1.01) gives

.01 - .0001/2 + .000001/3 - .00000001/4 + ...

~= .00995033... where successive modifications come after these 8 decimal places.

On the other side, for 2/201 = 1/100.5 = 10/1005:

        .00995024
-----------


1005 )10.00000000
       9 045
       -----
         9550
         9045
         ----
          5050
          5025
          ----
            2500
            2010
            ----
             4900
            

So ln(1.01) is larger.            


  Posted by Charlie on 2011-07-26 14:52:55
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