What is a fast way of adding all the numbers from 1 to 100 ?
i really need to find out the trick ASAP
please please please help
thans :) xx
- peateargryfinLv 59 years agoFavorite Answer
Imagine a square 4 * 4 dots in size
You can split it diagonally into two triangles of the same size and a diagonal
The number of dots in the square is 4*4 = 16
The number of dots along the diagonal is 4
The remaining dots are 16 - 4 = 12 and since the triangles are the same size we can find the number by dividing 12 by 2 = 6
Say we want a slightly bigger triangle, one that includes the diagonal then the number of dots would be 6 + 4 = 10
Why do these dots and triangles matter?
The triangle has 1 dot in the first row, 2 in the second, 3 in the third etc. so knowing the number of dots in the triangle here tells us the sum of 1, 2 and 3 = 6
More generally if when had a square with n dots by n dots there would be n² dots in total.
Along the diagonal there would be n dots, so both triangles would have (n² - n)/2
To create the bigger triangle:
(n² - n)/2 + n = (n² - n)/2 + 2n/2 = (n² - n + 2n)/2 = (n² + n)/2
This can be written as n(n+1)/2
In the case of n = 100 rows then there are 100*101/2 = 5050 dots which is also the sum from 1 to 100.
- 9 years ago
You can use the sum formula for arithmetic series
n=100 (No. of values)
d=1 (Difference between two consecutive values)
a1=1 (First value of series)
Sum=S= n/2 (2a1 + (n-1)(d))
S=100/2 (2 + 99(1))
- 9 years ago
tn-1=a+d(n-1) this is the formula
n/2(first term+last term)
- noodlenogginLv 69 years ago
all the numbers? ALL the numbers? Every bloomin' number?!!
would you be meaning: whole numbers, natural numbers, rational numbers, integers, squared numbers...???
need just a tad bit more information to provide a constructive answer. based on the information in the question, the 'fast way' would be pencil and paper.
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- mrwizard9090Lv 59 years ago
for N=any positive integer.