The cards show the even numbers 2, 4, 6, …, 40. Reorder the sum and pair the cards from the outside in: 2 with 40, 4 with 38, and so on. What is 2 + 4 + 6 + … + 40?

Question

Accepted Answer

420. There are 40 ÷ 2 = 20 cards, so 10 pairs. Each pair adds to 2 + 40 = 42. Sum = 10 × 42 = 420. Reordering is allowed because addition is commutative and associative. (840 counts 20 pairs; 462 counts 11 pairs.)

The cards show the even numbers 2, 4, 6, …, 40. Reorder the sum and pair the cards from the outside in: 2 with 40, 4 with 38, and so on. What is 2 + 4 + 6 + … + 40?

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