pls help me i dont know how to answer this problem

I

ineedhelpinmath

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Bored from answering the problem set, Jenny suddenly writes the natural numbers from 1 to 1001 in a row.

(a) Can the signs ”+” and ”-” be placed between the numbers in such a way that the value of the resulting expression is 100? If yes, show an example. If not, provide a mathematical reason why.


(b) How about -499? If yes, show an example. If not, show the reason why.

Thank you very much! huhuhuh
 
What is the sum of all 1001 numbers?

What happens to the sum when you change a + to a -?
 
Would "1+2-3+4-5-6+7+8...", or any other mix of "+" and "-" be allowed? If so then this would be a pretty difficult question. Where did you get the question from? If a teacher gave you the question, then what are you studying in class?

With this interpretation then looking at parity helps with part a:-

1 odd
1±2 odd
1±2±3 even
1±2±3±4 even
1±2±3±4±5 odd
1±2±3±4±5±6 odd
1±2±3±4±5±6±7 even
...

Extrapolating this gives "1±2±...±1001" must have an odd result, therefore 100 is not possible
 
What have you tried? You have to try something. Show us your work so that we can give you some ideas to get what you want.

Note that (1-2) + (-3+4) = 0. In fact (1-2)+(-3+4) + (5-6) + (-7+8) + (9-10) + (-11 + 12) = 0. That is, 1-2-3+4+5-6-7+8+9-10 -11+12=0. Maybe you can use this idea to get the sum to be 100?
 
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Concerning part b) I have found a way of obtaining -499, by basically using @Jomo 's idea of just trying things.

EDIT: I might have cheated because my idea involved putting a "-" before the first "1", and the original question says the symbols are to be "placed between the numbers"
 
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Dr.Peterson said:
What is the sum of all 1001 numbers?

What happens to the sum when you change a + to a -?
Click to expand...
ineedhelpinmath said:
are those what the questions mean??
Click to expand...
I'm not sure what you' re asking, but I'll show you more directly what I have in mind.

Suppose the problem had been smaller:

Bored from answering the problem set, Jenny suddenly writes the natural numbers from 1 to 10 in a row.​
​
(a) Can the signs ”+” and ”-” be placed between the numbers in such a way that the value of the resulting expression is 10? If yes, show an example. If not, provide a mathematical reason why.​

If we just write 1+2+3+4+5+6+7+8+9+10, we get 55. If we change, say, + 10 to - 10, we subtract 20 from the total (because -10 is 20less than +10), and it becomes 35.

What kind of number can't we get, no matter where we put a - ?
 
Jomo said:
You do know that Jomo's idea is quite famous and named after me.
Click to expand...

I've been missing out on "Jomo's idea".

I just didn't want to claim that I was the first person to suggest actually trying something. Because it's an easy thing to forget when faced with a problem. I normally prefer going straight to the solution ?
 
OP, my post #10 was not aimed specifically at you - it is a general thing that people don't post their work, and Jomo is very good at asking people to show their thinking. So this was an "in joke". Please don't let it put you off posting your work even if it is wrong.

I'll give a hint that I have now found a non-cheating solution to part b (it was very similar to my cheating solution actually!)
 
Here is a hint for part (b). Consider my simpler case again:

Dr.Peterson said:
Suppose the problem had been smaller:

Bored from answering the problem set, Jenny suddenly writes the natural numbers from 1 to 10 in a row.​
​
(a) Can the signs ”+” and ”-” be placed between the numbers in such a way that the value of the resulting expression is 10? If yes, show an example. If not, provide a mathematical reason why.​

If we just write 1+2+3+4+5+6+7+8+9+10, we get 55. If we change, say, + 10 to - 10, we subtract 20 from the total (because -10 is 20less than +10), and it becomes 35.
Click to expand...
My part (b) might be,

(b) How about -45? If yes, show an example. If not, show the reason why.​

To change the sum from 55 to -45, we have to subtract a total of 100. That means we have to change the sign on numbers whose sum is 50. That's easy.
 
Let's look at this in the way that Dr Peterson is suggesting.

1 + 2 + 3 + ... + 1001 = 1001* 501 = 501501

Now if you (cheat, as Cubist puts it and) change 1 to -1, the total decreases by 2. If you change +2 to -2, the sum decreases by 4. If you change +3 to -3, then the sum decreases by 6. .... This shows that you can decrease the sum by 2 or 4 or 6 or..., that is by any even value up to 2002. Possibly as cubist suggest you can't change the 1 to -1, so you can decrease the sum by any even number above 2 up to 2002.

Now the problem should be easier to do. Can you please try?
 
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For part b, let's go the other way.

-1-2-3-4-...-1001= -501501. If we carefully picked a number and changed the neg sign to a pos sign then we can add any even number up to a certain point.

If that 1st number has to be 1 (after all it does say to put + or - between numbers!), then 1-2-3-4-...-1001 = -501499. Is there an even number (which might be a sum of even numbers) that you can add to -501499 to get -499?
 
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