1st Week EMC (2nd Meeting Class)
Topic : Story of Gauss
If you have a task to sum up all the number from 1 to 100, can you do it?
There is a mathematican called Gauss that have a faster way to sum up number from 1 to 100.
He do it with add the first number and last number, second number and second last number,
and so on. In this case, it would be like this :
1 + 2 + 3 + 4 + 5 + …………. + 100
(1 + 100) + (2 + 99) + (3 + 98) + ………… (50 + 51)
101 + 101 + 101 + 101 + ………….. + 101
With the new method, we have number 101 as many as 50. So, to know the sum of all
number 1 until 100, we just need to multiple 50 by 101
101 x 50 = 5050
So, the sum of number from 1 until 100 is 5050
Now, take a look at these problems
1. Find the value of
1+2+3+4+5+6+7+8
Analysis :
We can make 4 pairs of 9.
1+8=9
2+7=9
3+6=9
4+5=9
Instead of adding up all the numbers, we simply multiply 4 by 9
4 x 9 = 36
2. Find the value of
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
Analysis :
We can make 5 pairs of 11.
1 + 10 = 11
2 + 9 = 11
3 + 8 = 11
4 + 7 = 11
5 + 6 = 11
Instead of adding up all the numbers, we multiply 5 by 11
5 x 11 = 55
3. Find the value of
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15.
Analysis :
We can make 7 pairs of 16.
1 + 15 = 16
2 + 14 = 16
3 + 13 = 16
4 + 12 = 16
5 + 11 = 16
6 + 10 = 16
7 + 9 = 16
Now, what about the number that is not in pairs?
We just have to add the remaining number to the product of the pairs.
7 × 16 = 112
112 + 8 = 120
In some situations where you need to find the remaining number, just take the sum of the
first and last numbers in the sequence to divide by 2.
Story of Gauss Practice A
1. Find the sum of :
a. 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
b. 10 + 30 + 50 + 70 + 90 + 110
c. 7 + 20 + 34 + 48 + 62 + 76 + 90
d. 1 + 11 + 21 + 31 + 41 + 51
e. 44 + 88 + 132 + 176 + 210 + 254
2. Dewi celebrates her birthday every year. On her 12th birthday, she wants to know
how many candles she has used in total from her 1st to her 12th birthday.
How many candles has she used in total?