|Name: jo that is asking: student Level the the question: an additional |
Question: what is the sum of the first 100 totality numbers?? how am i an alleged to job-related this the end efficiently? thanks
The question you asked relates ago to a famed mathematician, Gauss. In elementary college in the late 1700’s, Gauss to be asked to uncover the sum of the numbers from 1 come 100. The question was assigned together “busy work” through the teacher, however Gauss found the price rather easily by finding out a pattern. His monitoring was as follows:
1 + 2 + 3 + 4 + … + 98 + 99 + 100
Gauss noticed that if he was to break-up the numbers right into two teams (1 to 50 and also 51 to 100), the could add them with each other vertically to gain a amount of 101.
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 that his final complete would be 50(101) = 5050.
The succession of numbers (1, 2, 3, … , 100) is arithmetic and also when us are in search of the sum of a sequence, we call it a series. Thanks to Gauss, over there is a distinct formula we have the right to use to find the sum of a series:
S is the amount of the series and n is the number of terms in the series, in this case, 100.
Hope this helps!
There room other means to resolve this problem. Girlfriend can, because that example, memorize the formula
This is an arithmetic series, because that which the formula is: S = n<2a+(n-1)d>/2 wherein a is the first term, d is the difference between terms, and n is the variety of terms. Because that the amount of the very first 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 also use one-of-a-kind properties that the particular sequence friend have.
An advantage of utilizing Gauss" technique is the you don"t have to memorize a formula, but what do you do if there room an odd variety of terms to add so friend can"t separation them into two groups, for instance "what is the sum of the very first 21 whole numbers?" Again we write the sequence "forwards and also backwards" yet using the entire sequence.