We have to assume that you're talking about whole numbers.
The sum is 5,050 .
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You do not need a conjecture; you can calculate the answer. The answer is 10,100
The first ten positive numbers total 55.
The sum of the squares of the first 100 natural numbers [1..100] is 338350, while the sum of the first 100 natural numbers squared is 25502500.
The sum is 17.
141,000