# Difference between revisions of "2013 AMC 12A Problems/Problem 21"

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## Revision as of 21:58, 13 February 2013

## 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 our original definition of .

However, at , going further than our second approximation will not distinguish between our answer choices.

So we take our second approximation and plug in.

Since , we know . This gives us our answer range: