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Legend has it that the great mathematician carl friedrich gauss ​(1777dash–​1855) at a very young age was told by his teacher to find the sum of the first 100 counting numbers. while his classmates toiled at the​ problem, carl simply wrote down a single number and handed the correct answer in to his teacher. the young carl explained that he observed that there were 50 pairs of numbers that each added up to 101. so the sum of all the numbers must be 50 times •101equals=5050. modify the procedure of gauss to find the sum. 1plus+2plus+3plus+...plus+320

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The procedure used by Carl Friedrich Gauss to find the sum of the first 100 counting numbers can be modified to find the sum of the numbers from 1 to 320. To do this, we need to find the number of pairs of numbers that add up to a constant value. In the case of the first 100 counting numbers, Gauss observed that there were 50 pairs of numbers that each added up to 101. To find the sum of the numbers from 1 to 320, we can use a similar approach. We need to find the constant value to which we can pair up the numbers. First, we find the sum of the first and last numbers: 1 + 320 = 321. Then, we find the sum of the second and second-to-last numbers: 2 + 319 = 321. We continue this process until we reach the middle number. Since there are an even number of terms (320 in this case), we can pair up 160 pairs of numbers. Each pair adds up to 321. Now, we can find the sum by multiplying the constant value by the number of pairs: 321 * 160 = 51,360. Therefore, the sum of the numbers from 1 to 320 is 51,360.

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Answer: Sum is 51360

Explanation: I have heard same legend and it is also told in hih school math books.

There are 160 pairs numbers which sum is 321, also (320 +1) + (319+2) + ... + (160 + 161). So sum is 160·321

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