What is the formula for when you add 1 + 2 + 3 + 4 up to 100?

Question

I learn this in High School and now its stuck in head looking for that formula, I know the answer is 5500 or is it 5550?

Answer 1

as the story goes, Gauss did this in elementary school. Write the sum in one direction, then in the reverse direction. Then add vertically:

1 + 2 + 3 + ..... n-1 + n
n+n-1+n-2 + ..... 2 + 1
------------------------------
(n+1)+(n+1)+......+(n+1)+(n+1)

Now adding across, there are n x (n+1). But we added each number twice, so we need to divide by two.

n(n+1)/2

Answer 2

1 +2 +3 +... 98 +99 +100
can be rewritten as
(1 +100) +(2 +99) +(3+98) +....
101 +101 +101 +...
There will be 50 groups of 101, so the sum becomes
50*101 =5050

The general method for an arithmetic series is to add the first and last number together, multiply that by how many numbers are in the series and dividing by 2.

For example,
7 +9 +11 + 13 +15 +17
(7+17)*6/2 =72

Answer 3

The sum for 1 + 2 + 3 + .... + n
is n(n+1)/2
So (100*101) / 2 = 5050

Answer 4

the average of the first and last values, times the number of values being added.

Summation from 1 to 100 = 100*[(1+100)/2] = 5050

Answer 5

n(n+1)/2 where n is the last number in the chain