Gaussian molecular formula: numbers from 1 to 100 add – how it works

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What is the result when you add the numbers from 100 to 100? This sounds tricky, but it is not really. For this calculation, there is a simple trick &# 8211; and even has its own name: The Gaussian sum formula, named after the famous German mathematician. We show in this guide, as you correctly adds the numbers from 1 to 100 and how the Gaussian sum formula works.

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The Internet and especially on social networks such as Facebook brainteasers and puzzles will be posted again and again, who already so make users driven to distraction. Recently, the Facebook puzzle made with the 3 for smoking heads &# 8211; Another one popular task is behind the somewhat unwieldy name Gausche molecular formula. The task is as follows: What is the result when one adds the numbers from 1 to 100? Even in the popular quiz show Millionaire failed a candidate recently on this question. Do you know the solution?

Gaussian molecular formula ExampleThe Gaussian sum formula as a mathematical equation. Source: Wikipedia

Gaussian sum formula &# 8211; Numbers from 1 to 100 added: What results mean?

Of course one could now begin in order to add all the numbers, that is along the lines of &# 8220; 1 + 2 + 3 + 4, etc.&# 8221 ;. The course would take too long and would also be quite expensive &# 8211; that's why many people also give directly. In reality, there is but one with the calculation can facilitate a simple trick. Just this ever first: When you come together is one of the numbers from 1 to 100, is the result 5050.

So you come to this number:

  • Rather than add the numbers in sequence (1 + 2 + 3 + 4, etc.) it is added in each case the the first and the last number.
  • It looks as follows: 100 + 1, 99 + 2, 98 + 3, etc., up to 50 + 51st The result is in any case one hundred and first
  • Overall, you get away with it on 50 pairs of numbers, each providing the sum of one hundred and first
  • To get to the result, so you have to then multiply only 50 x one hundred and first The result is the 5050th

Pretty clever the whole thing, right? Of course, this trick has long been known &# 8211; the first one came out, the German mathematician Carl Friedrich Gauß was. According to him, it is then called and known as Gaussian sum formula.

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Gaussian molecular formula: The behind it

According to tradition, Gauss to this formula at the tender age of 9 years have recognized. To immobilize the boy to his former mathematics teacher Büttner have put a difficult task to him, which he accepted that the young Gauss could solve them only after much deliberation. The story is narrated by the friend and colleague of Gauss, Wolfgang Sartorius von Waltershausen:

&# 8220; The young Gauss was hardly occurred in the computing class, as Buttner gave the summation of an arithmetic progression. The task, however, was hardly finished as Gauss raises the board with the language spoken in the lowly Brunswick dialect words on the table, "Ligget se '' At the end of the hour to the computing boards were reversed;. (As is her.) with a single number was from Gauss above and as Büttner tested the example, was found to the his own amazement of everyone present to be correct, while many of the rest were wrong and soon rectified with the Karwatsche (leather whip) (chastened) were.&# 8221;

Whether Gauss had just add the numbers from 1 to 100, is not known. In any case, the teacher recognized the boy's talent and promoted in the aftermath of which his unusual mathematical talent. The Gaussian sum formula is sometimes called &# 8220; less gauss&# 8221; designated.

You want more math? Read also with us what the solution to the math problem: 9-3 ÷ 1.3 + 1st We also show you also how you can calculate the Bachelor note and the general grade point average.

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