l>What is the sum of the first 100 whole numbers?
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Name: jo who is asking: student Level of the question: an additional

Question: what is the amount of the an initial 100 totality numbers?? how am i claimed to occupational this the end efficiently? thanks

Hi Jo,

The concern you request relates ago to a famous mathematician, Gauss. In elementary institution in the late 1700’s, Gauss to be asked to find the amount of the numbers from 1 come 100. The inquiry was assigned as “busy work” through the teacher, but Gauss discovered the price rather quickly by learning a pattern. His observation was as follows:

1 + 2 + 3 + 4 + … + 98 + 99 + 100

Gauss noticed the if he was to split the numbers right into two teams (1 come 50 and 51 come 100), he could include them together vertically to gain a amount of 101.

You are watching: Find the sum of integers from 1 to 100

1 + 2 + 3 + 4 + 5 + … + 48 + 49 + 50

100 + 99 + 98 + 97 + 96 + … + 53 + 52 + 51

1 + 100 = 101 2 + 99 = 101 3 + 98 = 101 . . . 48 + 53 = 101 49 + 52 = 101 50 + 51 = 101

Gauss realized then that his final full would it is in 50(101) = 5050.

The succession of numbers (1, 2, 3, … , 100) is arithmetic and when us are looking for the amount of a sequence, we speak to it a series. Thanks to Gauss, over there is a distinct formula we deserve to use to discover the sum of a series:

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S is the sum of the series and n is the number of terms in the series, in this case, 100.

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Hope this helps!

There room other means to settle this problem. Friend can, for example, memorize the formula

This is one arithmetic series, because that which the formula is: S = n<2a+(n-1)d>/2 wherein a is the an initial term, d is the difference between terms, and also n is the variety of terms. For the amount of the first 100 whole numbers: a = 1, d = 1, and also n = 100 Therefore, sub into the formula: S = 100<2(1)+(100-1)(1)>/2 = 100<101>/2 = 5050

You can additionally use unique properties that the particular sequence friend have.

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An benefit of using Gauss" method is the you don"t need to memorize a formula, however what perform you do if there room an odd variety of terms to add so you can"t separation them right into two groups, for example "what is the amount of the an initial 21 totality numbers?" Again we compose the sequence "forwards and also backwards" but using the whole sequence.