Challenge Yourself: Count and Add 1-100 Without a Calculator!

[konartist]

Can you count and add all the numbers 1-100 without using a calculator?

 

[kant]

Can you count and add all the numbers 1-100 without using a calculator?

You got me!

 

[VietDao29]

As a metter of fact, I think I can
If I am not mistaken then Gauss did it centuries ago...

 

[davee123]

Can you count and add all the numbers 1-100 without using a calculator?

Let's hope not! ... Maybe all the *integers*, tho :)
(And yeah, you can use the old ((S+F)/2)*(F-S+1) trick to add all the integers between S and F)[/color]

DaveE

 

[Jimmy Snyder]

Can you count and add all the numbers 1-100 without using a calculator?

Well it wasn't easy, but there are 100[/color] of them.

 

[konartist]

As a metter of fact, I think I can
If I am not mistaken then Gauss did it centuries ago...

Yes sir, an old wive's tale is that he one day was punished in 3rd grade class and the teacher asked him to add all the numbers 1-100 thinking it would keep him busy, but he was able to reply the answer back to her in a matter of seconds.

 

[michealsmith]

yea u just use the formula...sum = 0.5n(n+1)

so 0.5 x 100 x 101 =50 x 101 = 5050

 

[AKG]

Yes, 1 + ... + 100 = (1 + 100) + (2 + 99) + ... (50 + 51) = (101) + (101) + ... + (101) [50 times] = 50 x 101 = 5050. I heard that this is how Gauss did it.

 

[Cybersteve]

So what you're all saying is, find the average value (50.5) and mutiply by the number of terms.

 

[mattmns]

So what you're all saying is, find the average value (50.5) and mutiply by the number of terms.

What is 50.5 the average value of?

 

[VietDao29]

What is 50.5 the average value of?

I think he meant the average value of the first term and the last term, ie:
(1 + 100) / 2 = 50.5

 

[Cybersteve]

What is 50.5 the average value of?

50.5 is the average value of all the numbers 1 to 100 inclusive.

If there were an odd number of terms in an evenly spaced sequence the average would be the middle term.
As this sequence is even the average value is the average of the two middle terms - 50 & 51.

 

[mattmns]

Ahh, I must have misread something.

 

[Jimmy Snyder]

Ahh, I must have misread something.

Not so much misread as partially read. 50.5 is not only the average of 1 and 100. It is also the average of 2 and 99, 3 and 98, etc. That is, it is the average of the set of integers from 1 to 100.

 

[Zygotic Embryo]

im lost...

 

[Mk]

This is easy.

Here is a lecture that shows you how to do it.
http://www.jimloy.com/algebra/gauss.htm