l>What is the amount of the first 100 entirety numbers?
*
*
Name: jo that is asking: college student Level the the question: second

Question: what is the sum of the very first 100 whole numbers?? just how am i supposed to work this the end efficiently? thanks

Hi Jo,

The concern you asked relates ago to a famous mathematician, Gauss. In elementary college in the late 1700’s, Gauss was asked to uncover the amount of the numbers from 1 come 100. The question was assigned together “busy work” by the teacher, but Gauss uncovered the price rather conveniently by learning a pattern. His monitoring was together follows:

1 + 2 + 3 + 4 + … + 98 + 99 + 100

Gauss noticed that if he to be to break-up the numbers right into two teams (1 to 50 and also 51 to 100), that could include them together vertically to get a sum of 101.

You are watching: 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 establish then the his final complete would it is in 50(101) = 5050.

The succession of numbers (1, 2, 3, … , 100) is arithmetic and also when us are in search of the amount of a sequence, we contact it a series. Thanks to Gauss, over there is a special formula we can use to discover the amount of a series:

*

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

*

Hope this helps!

There are other means to fix this problem. Friend can, for example, memorize the formula

This is an arithmetic series, because that which the formula is: S = n<2a+(n-1)d>/2 whereby a is the first term, d is the difference in between terms, and also n is the number of terms. Because that the amount of the an initial 100 entirety 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 the the details sequence you have.

See more: What Is 3/4 Equivalent To R, Equivalent Fractions For 3/4

An advantage of using Gauss" method is that you don"t have to memorize a formula, however what perform you do if there are an odd number of terms to include so friend can"t split them into two groups, for instance "what is the amount of the an initial 21 entirety numbers?" Again we write the succession "forwards and backwards" yet using the whole sequence.