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What is the remainder when 2 + 4 + 6 + ... + 100 + 102 + 104 is divided by 7?

 Apr 30, 2021
 #1
avatar+2127 
+1

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

 

=^._.^=

 Apr 30, 2021
 #2
avatar+742 
+1

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

 

laugh

 Apr 30, 2021

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