The answer is the 100th triangular number so you can use the formula (n(n+1))/2.
n = 100 so the sum is (100 x 101)/2 = 10100/2 = 5,050.
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You do not need a conjecture; you can calculate the answer. The answer is 10,100
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 formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.
This is very easy. Simply square the number: 100 squared (100 x 100) = 10,000. So, the sum of the first 100 odd numbers is 10,000.
100