2008 iTest Problems/Problem 61
Revision as of 13:54, 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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