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EzraMethod 1 (Sum of the first n numbers): The sum of the first n positive integers is n(1 + n)/2 So the sum would be 1,000,000 * (1,000,001)/2 = 500,000,500,000. Method 2 (Algebraic Solution): Let x be the sum of the numbers 1 through 1,000,000. x = 1 + 2 + ... + 999,999 + 1,000,000. x = 1,000,000 + 999,999 + ... + 2 + 1 Adding these equations gives: 2x = 1,000,001 + 1,000,001 + ... + 1,000,001 + 1,000,001 Note that there are 1,000,000 different 1,000,001's in the above equation. So: 2x = 1,000,001(1,000,000) = 1,000,001,000,000 x = 500,000,500,000.
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Find the difference between the sum of the first 1000000 positive even numbers and the sum of the first 1000000 positive odd numbers?
The sum of the first 1,000,000 positive even numbers is: 2 + 4 + 6 + 8 + ... + 2,000,000 The sum of the first 1,000,000 positive odd integers is: 1 + 3 + 5 + 7 + ... + 1,999,999 The difference between the two is: (2-1) + (4-3) + (6-5) + (8-7) + ... + (2,000,000-1,999,999). This is the same as: 1 + 1 + 1 + 1 + ... + 1. Well how many 1's are there? 1,000,000. So the difference is 1,000,000. Note that if the question asked for the difference between the sum of the first 1,000 positive even numbers and the sum of the first 1,000 positive odd numbers, the answer would be 1,000. The first n even numbers and odd numbers? n.
What four numbers 1 through 9 make the sum of 23?
3,5,7,8
The sum of two numbers is k Find the minimum value of the sum of their cubes?
1
What two positive integers whose product is 32 have the greatest sum?
The numbers 32 and 1 (32 x 1 = 32) sum to 33. The numbers 4 and 8 (4 x 8 = 32) sum to 12 The numbers 2 and 16 (2 x 16 = 32) sum to 18. There are no other factors which are integers, so 32 and 1 is the answer.
What is the sum of all the odd numbers from 1 to 100?
over 50
