Q:

What is the sum of the first 100 even numbers?

A:

The sum of the first 100 even numbers is 10,100. This is calculated by taking the sum of the first 100 numbers, which is 5,050, and multiplying by 2. To find the total of the first 100 numbers, multiply 50 by 101.

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The calculation for the first 100 numbers is based on a legend of mathematician Carl Friedrich Gauss. According to the story, as a child his teacher asked the class to find the sum of the first 100 numbers to keep them busy. Gauss was able to determine it was 5,050 in a few seconds. He realized that the sum of the first and last number was 101, the second number and the second to last number was 101, and so on, resulting in 50 pairs of 101. He then multiplied 50 by 101 to get 5,050. Since the sum of the first 100 even numbers is double that of the first 100, a person can multiply 5,050 by 2 to get 10,100.

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