Jenny writes the natural numbers from 1 to 1001 in a row.
- 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.
- How about -499? If yes, show an example. If not, show the reason why.
I'm not entirely sure what the question means. Is it expecting me to be able to write down every number from 1 to 1001 and then do this by trial and error. There has to be a better way to do it right?
Hint:
1)When you $1\pm 2$ you get an odd number, now what number odd or even do you get when you add or subtract $3$, then $4$ and so on. Can you establish a pattern?
2) So the sum is $-499$ We know that the numbers can be partitioned into $500$ pairs and $1$ lone number. Do you notice that $-500+1=499$
Can you find that lone number, and also the relationship between the numbers which are in the same pair?