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Title: Exercises solved with Gauss Sum
Description: These notes include some exercises solved with Gauss Sum. They are fully solved, step-by-step. In this document are all types of exercises with Gauss Sum. My notes are aimed at the 2nd and 3rd years.
Description: These notes include some exercises solved with Gauss Sum. They are fully solved, step-by-step. In this document are all types of exercises with Gauss Sum. My notes are aimed at the 2nd and 3rd years.
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Exercises solved with Gauss sum
Exercice 1
...
+ 100;
(1)
b) S2 = 2 + 4 + 6 +
...
+ 99;
(3)
Solutions:
a) S1 = 100 · (100 + 1) : 2 = 100 · 101 : 2 = 10100 : 2 = 5050;
b) Firstly, we will compute the numbers of terms: (100-2):2+1=98:2+1=50 after this
we will find the value of sum;
S2 = (100 + 2) · 50 : 2 = 102 · 50 : 2 = 100 · 51 : 2 = 5100 : 2 = 2550;
c) The number of terms is:(99 - 1):2+1= 98:2+1=50;
In these conditions, we can find the sum: S3 = (1 + 99) · 50 : 2 = 100 · 50 : 2 = 5000 :
2 = 2500;
Exercise 2
...
+ 184;
(4)
b) S5 = 7 + 16 + 25 +
...
+ 436;
(6)
Solutions:
a) We will find firstly the numbers of terms: (184-79):3+1= 105:3+1= 36
...
In these conditions we
will compute the sum:
S5 = (7 + 862) · 96 : 2 = 869 · 48 = 41712;
c) The sum have 436-100+1=336+1=337 terms, and we can compute it in this way:
S6 = (100 + 436) · 337 : 2 = 536 · 337 : 2 = 536 : 2 · 337 = 268 · 337 = 90316;
Exercise 3
...
+ 363;
(7)
b) S8 = 81 + 86 + 91 +
...
+ 583;
(9)
Solutions:
a) Firstly, we will find the numbers of terms : (363-99):6+1= 264:6+1= 44+1= 45
...
Because we know the numbers of terms, we can compute the sum:
S8 = (81 + 361) · 57 : 2 = 442 · 57 : 2 = 442 : 2 · 57 = 221 · 57 = 12597;
c) Firstly, we will compute the numbers of terms: (583-2):7+1= 581:7+1= 83+1=
84, after this we can find the sum:
S9 = (2 + 593) · 84 : 2 = 595 · 84 : 2 = 595 · 42 = 24990;
1
Title: Exercises solved with Gauss Sum
Description: These notes include some exercises solved with Gauss Sum. They are fully solved, step-by-step. In this document are all types of exercises with Gauss Sum. My notes are aimed at the 2nd and 3rd years.
Description: These notes include some exercises solved with Gauss Sum. They are fully solved, step-by-step. In this document are all types of exercises with Gauss Sum. My notes are aimed at the 2nd and 3rd years.