**For example:**(1 + 100), (2 + 99), (3 + 98), . . . , and each pair has a sum of 101.

Carl Gauss was a German Scientist and mathematician. He made many important discoveries in the field of science and math. It is believed that he showed a talent for math at the age of seven. Carl Gauss used a different approach for sums discussed in this article.

**Gauss elimination method** is used to solve a system of linear equations. He amazed his teacher with how quickly he found the sum of the integers from 1 to 100 to be 5,050.

💡For example:(1 + 100), (2 + 99), (3 + 98), . . . , and each pair has a sum of 101.

**50 pairs × 101 (the sum of each pair) = 5,050.**

Another way to represent the problem could be to list the integers from 1 to 100 and write the same list in reverse order below the first list.

1. Compute 1 + 2 + 3 + 4 + 5 using gauss method of elimination.

Let’s club the numbers using Gauss’s way.

(1 + 4 )+ (2 + 3) + (5)

5 + 5 + 5

Therefore, the sum of 1 + 2 + 3 + 4 + 5 is 15.

2. Compute 742 + 746 + 750 + 754 + 758 using gauss method of elimination.

3. Find the sum of all multiples of 4 that are smaller than or equal to 40 using gauss method of elimination.

4. Compute 1 + 2 + 3 + 4 + 5 +…+ 47 + 48 + 49 + 50 using gauss method of elimination.

**Step 1:** 1 + 50 = 2 + 49 = 3 + 48 = 4 + 47 = 51

**=> **50 ÷ 2 = 25 pairs of 51

**Step 2: **25 × 51 = (20 × 51) + (5 × 51)

=** **1,020 + 255

5. There are 10 rows of seats in an auditorium. The first row has 30 seats. The second row has 34 seats. The third row has 38 seats and so on. How many seats are there in the auditorium?

6. Find the sum of all multiples of 7 that are smaller than or equal to 70.

7. Compute 1 + 2 + 3 + 4 +…+ 19 + 20 using gauss method of elimination.

**Step 1: 1 + 20 = 2 + 19 = 3 + 18 = 4 + 17 = 21**

**= There are 10 pairs of 21**

**Step 2: 10 x 21 **

**= 210
**

8. Compute 100 – 99 + 98 – 97 + … + 4 – 3 + 2 – 1 using gauss method of elimination.

**Step 1: **100 – 99 = 98 – 97 = 4 – 3 = 2 – 1 = 1

**= **There are 50 1s

**Step 2: **50 x 1

= **50**

9. Compute 1 + 2 – 3 + 4 + 5 – 6 + 7 + 8 – 9 +…+ 28 + 29 – 30 using gauss method of elimination.

1 + 2 – 3 = 0

4 + 5 – 6 = 3

7 + 8 – 9 = 6

10 + 11 – 12 = 9

…

25 + 26 – 27 = 24 28 + 29 – 30 = 27

3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27

3 + 27 = 6 + 24 = 9 + 21 = 12 + 18 = 30

(4 x 30) + 15 = 120 + 15

= **135**

10. Determine the sum of the first 10 numbers of the set {5, 6, 7, 8, 9, 10, ...} using gauss method of elimination.

The first number is 5 while the 10th number is 14.

Using n = 10, the sum is

(10/2)(5 + 14) = (5)(19) = 95

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