What is the remainder when 2 + 4 + 6 + ... + 100 + 102 + 104 is divided by 7?
+2401 2, 4, 6, 1, 3, 5, 0, 2, 4, 6... (in mod 7)
Total of 52 numbers.
Each cycle of 7 numbers is 21, or 0.
50th, 51th, 52th number added is our answer. 2 + 4 + 6 = 12
12 mod 7 = 5
=^._.^=
+874 What is the remainder when 2 + 4 + 6 + ... + 100 + 102 + 104 is divided by 7?
2 + 4 + 6 + ... + 100 + 102 + 104 = 2(1 + 2 + 3 + ... + 50 + 51 + 52)
1 + 2 + 3 + ... + 50 + 51 + 52 = (52)(53)/2
2((52)(53)/2) = (52)(53)
52 mod 7 = 3
53 mod 7 = 4
52*53 mod 7 = 12
12 mod 7 = 5
