What is the unit digit of 1 5+ 2 5+ 3 5+ … + 20 5?
0
For any integer n, the unit digit of \(n^5\) equals the unit digit of n (cyclicity check for digits 0–9).
So the unit digit of the sum equals the unit digit of \(1+2+\cdots+20=\tfrac{20\times 21}{2}=210\).
Unit digit of 210 is 0.
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