# what’s 1 plus 2 plus 3 plus 4 plus 5… all the way to plus 1000?

please do not say i don’t know

• One way to solve this type of problem is to pair up the numbers. Let’s pretend the problem was to add up the numbers from 1 to 10. Let’s pair up the lowest and highest:

1 + 10 = 11

We’ll pair up the next lowest an next highest:

2 + 9 = 11

We continue in this fashion until they meet in the middle. All our pairs look like this:

1 + 10 = 11

2 + 9 = 11

3 + 8 =11

4 + 7 = 11

5 + 6 =11

What do you notice?

A) Each added pair equals 11

B) There are 5 pairs, which is half the highest number we started with:

10/2 = 5

Now we can multiply the number of pairs by the total of one of the pairs:

5 * 11 = 55

Let’s apply this technique to your problem.

1 + 1000 = 1001

2 + 999 = 1001

3 + 998 = 1001

………lots of other pairs………

498 + 503 = 1001

499 + 502 = 1001

500 + 501 = 1001

How many pairs are there?

1000 / 2 = 500

Now we can multiply the number of pairs by the total of one of the pairs:

500 * 1001 = 500,500

"what’s 1 plus 2 plus 3 plus 4 plus 5… all the way to plus 1000?"

• 1 Plus 2 Plus 3 Plus 4

• The sum of 1..N is (N²+N)÷2. In this case, that’s (1000²+1000)÷2 = (1000000+1000)÷2 = 1001000÷2 = 500500.

Memorize the formula.

• (number of terms)(first term + last term)/2

1 + 2 + 3 + 4 + 5 + … … + 1000

= 1000(1 + 1000)/2

= 1000(1001)/2

= 1001000/2

= 500500

• the "trick" is to see that 1+1000=1001

``                                     2+999=1001 etc ``

so you will get 1001*1000 if you add everynumber which is other one, but you will have counted everything double as you have 1+1000 but also 1000+1

so divide this by 2

so you get 1001 *500 so this is equal to 500500

• S = n(n+1) / 2

S = 1000(1000 + 1) / 2

S = 500500

Proof:

..1… +… 2.. +… 3.. +.. 4 …+ ..5 …+ …. + 1000 =

1000 + 998 + 997 + 996 + 995 + …… + 1

1001 + 1001 + 1001 + 1001 + 1001 + …+1001

1000(1001) = 1001000

1/2 (1001000) = 500500

The sum is 500500.

• First, find the average. Because the numbers are equally distributed, the average is halfway between 1000 and one: (1000+1)/2 = 500.5. Multiply the average by the number of numbers: 500.51000 = 500,500.

• (1+1000)1000/2= 500500

so the sum is 500500

• 500500

here’s my matlab code I wrote for it real quickly

sum = 0;

for i=1:1000

``````x = i;

sum = x + sum;``````

end

sum