Anonymous

# is it true that if you add 1-100 you will get 5000?

it was on a game board, but does that make it true? anyway, so it basically said that adding 1+2+3 and so on to 100 would get 5000. i did it and i have never gotten 5000, no mistakes either. do you know?

Relevance

If you add 1 to 100, you have 101. Then if you add 2 to 99, you also get 101.

See a pattern?

1 + 100

2 + 99

3 + 98

(...)

50 + 51

Basically, you have 50 operations that add to 101 each, so the total is 5050.

Yes I remember the question, add all the numbers from 1 through 10.

here is what the clever little girl did:

1+2+3+4+5+6+7+8+9+10

she added the first and the last 1+10=11

then she saw a pattern, the next, 2, and the next to last, 9 also =11

So, her very quick answer was 5 (11)=55

Now do the same, adding numbers from 1 to 100.

First, 1+100=101

There are 50 of those repetitions, so the answer is 50(101)=5050, not 5000

• Anonymous

No, but that's close. You will get 5050. Here's why:

Imagine you are looking at a piece of paper that has two columns of numbers. The first has all the numbers from 1-50 going up the page, the second has all the numbers from 51-100 going down. If you add up each pair of numbers (1 & 100, 2 & 99, 3 & 98, etc.), you will notice they will all add up to 101. As each column has 50 numbers, there will be 50 pairs of numbers that add up to 101. 50(101)=5050

There is a formula for this summation

S = [n(n+1)]/2

Where n is how high you're counting, in this case 100.

So let's plug in and see what happens

S = [100(100+1)]/2

S = [100(101)]/2

S = 50(101) [I divided 100 by 2 to get 50]

S = 5050

Just over 5000

• clewis
Lv 4
4 years ago

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SSDD is correct, Fungus forgot one.

1 + 99

2 + 98

3 + 97

....

49 + 51

That gives 49 100's. Then there is a 50 and the 100. = 4900 + 50 + 100 = 5050.

The easy way is to use the formula SSDD showed you.

• Anonymous

there is a formula for this

n(n+1)/2

where n is the number till which u are counting,

try it out

1+2+3+4= 10

n=4

4(4+1)/2 = 4x5/2 = 10 :)

so for 100, it is 100x101/2 which is 5050

EDIT :- Fungus, you are wrong. there are 50 100s and one fifty, that makes it 5050

• Anonymous

You can't add 1-100 to make 5000.

If you pair them up, there are 49 100s and a 50.

It should sum to 4950.