The sum of the first 30 positive even numbers is 930.
The sum of the first 100 positive even numbers is 10,100.
The sum of the first 30 positive even numbers is 930.
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There is no conjecture about the sum of the first 30 positive even numbers. The answer can be derived and proven. A statement that has been proven is no longer a conjecture.
The answer to what is the sum of the first positive even numbers is 930. It doesn't mean that you add all the even numbers up until you reach the number 30. In fact, since you have to get the sum of the even numbers, you have to add all even numbers until you get to the number 60.
The sum of the first 100 positive even numbers can be calculated using the formula for the sum of an arithmetic series: n*(first term + last term)/2. In this case, the first term is 2, the last term is 200, and n is 100. Therefore, the sum is 10,100.
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.
The sum of the first 15 positive even numbers is 240. (Simply square 15, then add 15 to the result: 15 x 15 = 225. 225 + 15 = 240).
The sum of the first seven positive INTEGERS is 28. The sum of the fisrt seven positive numbers is infinitesimally small.
The sum of the first six positive numbers (1 to 6) is 21.
You do not need a conjecture; you can calculate the answer. The answer is 10,100