1982 AHSME Problems/Problem 30
Problem
Find the units digit of the decimal expansion of
Solution
Let and Note that and are both integers: When we expand (Binomial Theorem) and combine like terms for each expression, the rational terms are added and the irrational terms are canceled.
We have Similarly, we have We add the two equations and take the sum modulo It is clear that from which We conclude that the units digit of the decimal expansion of is Since the units digit of the decimal expansion of is the units digit of the decimal expansion of is
~MRENTHUSIASM
See Also
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