unit digit
Number Theory
Level
2
Find the units digit of 2011! + 2012! + 2013! + 2014! + 2015!
The answer is 0.
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1 solution
As 2 is less than 5, then ⌈ 5 2 0 1 1 ⌉ + ⌈ 2 5 2 0 1 1 ⌉ + ⌈ 1 2 5 2 0 1 1 ⌉ + ⌈ 6 2 5 2 0 1 1 ⌉ = 4 0 2 + 8 0 + 1 6 + 3 = 5 0 1 implies that 2011! ends in 501 zeros. The same with 2012!, 2013! and 2014!. In fact, 2015! ends with 502 zeros