adding integers question for DD16

[Caropooh]

One of the questions on her homework is:
What is the sum of the first 1000 positive integers?
There has got to be a easy way of doing this, but I have no clue! (she doesn't seem to either!) HELP!!!

 

[abdmom]

*This sum of positive integers

 

[alexandria674]

I'm bad at math but the sum of the first 100 integers is 100 but "sum" means adding so you add the numbers all together?

 

[design_mom]

If you pair up the numbers using the lowest un-used integers and the highest unused integers, you always get the same number:
1 + 1000 = 1001
2 + 999 = 1001
3 + 998 = 1001, etc.
The middle set would be 500 + 501 = 1001.

So you've got 500 pairs of numbers, each totaling 1001. You can add them all up, or use multiplication: Your final answer would be 500 (number pairs) x 1001 (sum of each pair) = 500,500.

 

[abdmom]

I'm bad at math but the sum of the first 100 integers is 100?

Nope

 

[Sparx]

This is an arithmetic series.

http://www.mathwords.com/a/arithmetic_series.htm

That explains it pretty clearly.

 

[Caropooh]

If you pair up the numbers using the lowest un-used integers and the highest unused integers, you always get the same number:
1 + 1000 = 1001
2 + 999 = 1001
3 + 998 = 1001, etc.
The middle set would be 500 + 501 = 1001.

So you've got 500 pairs of numbers, each totaling 1001. You can add them all up, or use multiplication: Your final answer would be 500 (number pairs) x 1001 (sum of each pair) = 500,500.

This made sense to her! (I get a glazed eye look when it comes to math) Thanks!

 

[FireDancer]

You are looking for the summation of 1000. Get a calculator with a summation function on it. It is expressed with the ∑ symbol.

 

[Caropooh]

This is an arithmetic series.

http://www.mathwords.com/a/arithmetic_series.htm

That explains it pretty clearly.

thanks! That helped also!

 

[Mickey'snewestfan]

I'm bad at math but the sum of the first 100 integers is 100 but "sum" means adding so you add the numbers all together?

The sum of the first 100 integers can't possibly be 100, since you're adding 100 to 99 other numbers.

Here's how I'd figure it out -- I'd take the first 100 integers and add them this way . . . 100 + (99+1) + (98 + 2) . . . . + 50. That's the sum of the First 100 (we'll call it F)

Then I'd figure out the sum of the 2nd hundred (101 to 200) using the following formula {(100 x 100) + F}. (because it's basically F plus an extra 100 for each integer).

Then I'd figure out the sum of the 3rd hundred {(200 x 100) + F} . . . etc . . .

I'm purposely only doing about 1/2 the math to make your child do the work, but I'm sure you get the idea.

There may be a faster formula, but this one will really make your kid think about which numbers they're combining where, and the way mathematicians look for patterns.

 

[DISdreamin']

(n^2 + n)/2

where n is 1000.