Name: jo who is asking: student Level of the question: an additional Question: what is the sum of the an initial 100 entirety numbers?? just how am i an alleged to work-related this the end efficiently? thanks |

Hi Jo, The question you asked relates back to a famous mathematician, Gauss. In elementary school in the late 1700’s, Gauss to be asked to discover the sum of the number from 1 to 100. The inquiry was assigned as “busy work” by the teacher, however Gauss discovered the answer rather easily by discovering a pattern. His observation was as follows: 1 + 2 + 3 + 4 + … + 98 + 99 + 100 Gauss noticed that if he was to split the numbers into two teams (1 come 50 and 51 come 100), the could include them together vertically to gain a sum 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 realized then that his final complete would be 50(101) = 5050. The sequence of numbers (1, 2, 3, … , 100) is arithmetic and also when we are trying to find the sum of a sequence, we contact it a series. Thanks to Gauss, over there is a special formula we can use to uncover the sum of a series: S is the sum of the collection and n is the number of terms in the series, in this case, 100. Hope this helps! There space other ways to deal with 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 where a is the first term, d is the difference in between terms, and n is the variety of terms. Because that the amount of the an initial 100 whole numbers: a = 1, d = 1, and also n = 100 Therefore, sub right into the formula: S = 100<2(1)+(100-1)(1)>/2 = 100<101>/2 = 5050 You can also use distinct properties that the particular sequence you have. An advantage of using Gauss" an approach is that you don"t have to memorize a formula, however what execute you carry out if there space an odd number of terms to include so girlfriend can"t split them into two groups, for example "what is the amount of the an initial 21 whole numbers?" Again we create the sequence "forwards and backwards" yet using the entire sequence. |

# SUM OF ALL NUMBERS BETWEEN 1 AND 100

l>What is the amount of the very first 100 totality numbers?