2013 AMC 12A Problems/Problem 21
Revision as of 22:04, 13 February 2013 by Epicwisdom (talk | contribs) (Clarification and subscripts)
Solution
Let and , and from the problem description,
We can reason out an approximation, by ignoring the :
And a better approximation, by plugging in our first approximation for in our original definition for :
And an even better approximation:
Continuing this pattern, obviously, will eventually terminate at , in other words our original definition of .
However, at , going further than will not distinguish between our answer choices. is nearly indistinguishable from .
So we take and plug in.
Since , we know . This gives us our answer range: