there is a trick to work out 1 to 1000 added up.what is it?

Question

my head of maths department asked me.

Answer 1

Looks like a lot of people knew how to do this. I'd just like to note how polite everyone was. No one insulted poor sobrien. Of course, the poor guy is probably still punching numbers into his calculator. :-)

Answer 2

The sum of numbers from 1 to 10 is 55 divided by 5 =11 which is the same as folding the numbers ie taking 1 to 10 and adding the reverse order columns which all add to 11 then averaging the answer ie 11/2=5.5 this we can translate into x=x*((x+1)/2) which should give the right answer.

or
If you add 1 to 1,000, you get 1,001. Then simply visualize increasing by one from one side of the set of numbers and adding it to a decreased by one largest remaining number out of the series. You get 1,001 every time all the way to the final 2 numbers: 500 and 501. These final 2 numbers are the only numbers standing after you've added all the rest on the sides of each of those 2 numbers. You can tell they're the last 2 because they are right next to each other and add to 1,001. So the answer is 500 * 1,001 = 500,500.

Answer 3

Use the famous Gauss sum formula: n(n+1)/2, with n = 1000.
1000(1000+1)/2 = 500,500.

To understand how this formula is derived, consider the numbers ordered least to greatest. The sum of the first and the last, in this case, is 1 + 1,000 = 1,001. Then take 2 + 999 = 1,001. Likewise, 3 + 998 = 1,001. So you can see this pattern of summing the outer numbers always gets 1,001. Then you consider how many of these pairs there will be - it is half the number of the total numbers on the list. This is why the formula is (n+1)n/2

Answer 4

Okay, if you take 1000 + 1 you get 1001
If you take 999 + 2 you get 1001

All the way to 501+500 = 1001
so you can take 1001 and times it by 500 (1000/2)
=500500

Answer 5

1+1000=1001
2+999=1001
...
500+501=1001

The total of the sums on the Right Hand Side is 500500

Answer 6

yeah, you have to do it like this:
1.how many numbers are there between 1 and 1000, inclusive?
2.how much is the average of all those numbers?
3.multiply the average by the total number.

Alternate method:
1.Add the first and last number 1000+1
2.Add the second and second to last 999+2
3.Repeat until you get to 500+501

Answer 7

Ok, in one line write 1 to 1000, in the line under it write 1000 to 1. If u add numbers in every column, u will get 1001. Now multiply 1001 by 1000 and divide by 2. Here is your answer.:) We did it in Statistics class.

Answer 8

n(n+1)/2

Answer 9

0 + 1000 = 1000
1 + 999 = 1000
2 + 998 = 1000
3 + 997 = 1000

Continue doing this (500 times), until you reach 499 + 501 = 1000
Then just add 500 (cus it wasn't paired up) and you got the sum

So in cunclusion it's 500*1000 + 500

Answer 10

1+1000 = 1001
2+999 = 1001
...
500+501 = 1001

1001*500=500,500

Answer 11

yes sum upto n is n(n+1)/2
so 1+2+3+...1000= 1000*1001/2= 500500

I wonder if you are not aware of sum upto n digits: its so simple..you can even look for sum of squares up to n like 1^2+2^2+3^2;;;+n^2..try finding that too...