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.
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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 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 three even positive integers is 2 + 4 + 6 = 12.
You do not need a conjecture; you can calculate the answer. The answer is 10,100
even numbers are exactly divisible by two. ie. they do not give a remainder when divided by 2. natural numbers are positive integers starting from 1. even natural numbers are a combination of both.. eg. 2,4,50 etc the term positive is not required for these numbers because, natural numbers are positive !... so positive 'natural number' is like saying ' approximated estimate '..