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

9 Answers

  • 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?"

    The answer is 500,500

  • 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

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