2008 iTest Problems/Problem 61
Revision as of 12:54, 7 August 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 61 (credit to official solution) -- harder units digit problem)
Problem
Find the units digits in the decimal expansion of 
Solution
Let 
be a positive integer. Note that 
which is close to 
That means 
is close to zero. With this in mind, we find that 
is an integer, and the expansion is equal to 
To find that the units digit of , note that in the expansion of 
and 
most of the terms end in a 
That means the units digit equals the units digit of 
Now we need to find out how small 
is. With a calculator, we find that 
But even without a calculator, we can use inequalities to show that 
This means that 
would be close to
Thus, the units digit of the decimal expansion is 
See Also
| 2008 iTest (Problems) | ||
| Preceded by: Problem 60 |
Followed by: Problem 62 | |
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