Question

Find the last digit of the sum

0! + 2! + 4! +...+ 2010! + 2012!

Please show full steps answer.

Answer 1

By definition $5!=5\cdot4\cdot3\cdot2\cdot1=120$. Thus, for all numbers of the sum that are greater than $5!$ (those numbers are $6!,7!,...$ ) the last digit is 0. Thus, it is enough to compute the sum of the following terms: $0!+1!+2!+3!+4!=1+1+4+6+24=36$. Thus, the last digit of the sum is 6.

Answer: 6.