Question

How do you workout the last digit of the sum for:
0 + 1 + 2 + 3 + 4 + . . . + 91 + 92 + 93 + 94?

Answer 1

the easy way is to only add up the last digits
the first 10 are
0,1,2,3,4,5,6,7,8,9
then it starts over
repeats 9 times
then it does 1,2,3,4
so we find 0+1+2+3+4+5+6+7+8+9 and m ultiply by 9
then add 1+2+3+4

0+1+2+3+4+5+6+7+8+9=45
we only need th last dgit so
5 times 9=45
we need the last digit
5

then add that to 1+2+3+4=10
15
15+5=0
answer is 0 is the last digit

Answer 2

Well,

If we remember what a certain Gauss did when adding the natural numbers up to 100, we can remember that he ended up with pairs of 101.  1 + 100, 2 + 99, 3 + 98, etc.  Likewise, we can do this with this pattern, making pairs of 94.

0 + 94, 1 + 93, 2 + 92...45 + 47

We are left with 46.

Notice that we have 46 pairs of 94 plus an extra 46.

Thus, we can just multiply 46 by 94 and add 46.

46(94) + 46
4324 + 46
4370

The last digit is zero.