2000 AMC 8 Problems/Problem 14
Problem
What is the units digit of ?
Video Solution
https://youtu.be/7an5wU9Q5hk?t=1552
Solution
Finding a pattern for each half of the sum, even powers of have a units digit of , and odd powers of have a units digit of . So, has a units digit of .
Powers of have the exact same property, so also has a units digit of . which has a units digit of , so the answer is .
Solution 2
Using modular arithmetic:
Similarly,
We have
-ryjs
Solution 3
Experimentation gives
Using this we have
Both and are odd, so we are left with which has units digit -ryjs
See Also
2000 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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