How to add the symbol to 0 for natural numbers from 1 to 1998?

In the number 1, 2, 3 ,..., 1998 with the symbols "+" and "-" and calculated sequentially, what is the smallest possible non-negative number?

Analysis To get the smallest non-negative number, it is necessary to produce as many "0s" as possible by adding a reasonable sign

1+2+3+…+1998 = is an odd number, again at 1, 2, 3 ,...The addition of the symbols "+" and "-" before 1998 does not change the odd and even numbers of their algebraic sums, so the resulting minimum non-negative number will not be less than 1.

First, consider how to add symbols between the four consecutive natural numbers n, n+1, n+2, and n+3 to make them algebraically minimized.

It is clear that n-(n+1)-(n+2)+(n+3)=0

So we will ,... 1, 2, 3In 1998, each adjacent four are divided into a group, and then the symbol is added according to the above method, that is, (-1+2)+(3-4-5+6)+7-8-9+10)+....1995-1996-1997+1998)= -1+2=1

Therefore, the smallest non-negative number is 1.

So there is no solution.

There should be no solution to this, as evidenced by the following:

1-2-3+4=0;That is, the sum of the two additions at each end of the four numbers minus the middle two is 0;

So every four numbers can clear 0 once, but 1998 4 = 499....2, so it can't be 0

Summary. Natural numbers from 1 to 50 are written consecutively. Placing the symbol "+" or "-" between them results in 0. This is what to ask.

Natural numbers from 1 to 50 are written consecutively. Placing the symbol "+" or "-" between them results in 0.

Natural numbers from 1 to 50 are written consecutively. Placing the symbol "+" or "-" between them results in 0. This is what to ask.

1-50 or the result should be equal to 0

1-2+3-4+5-6+7-8+9-10+11-12+..48-49+50=0 Add up the digital manuscript covers at both ends of the key: it becomes (1+50)+(2-49)+(3+48)...

25-26)=0 and then the reed tease becomes 51-51 + 51-51 + 51-51....0

So why did I end up with a 51?

You do the math again.

This one is exactly 25 pairs.

After offsetting, it is 0

Summary. 1+51-(2+49)+3+48-(4+47)+5+46-(6+45)+24+27-(25+26) 0 can be obtained in pairs of twos.

Natural numbers from 1 to 50 are written consecutively. Placing the symbol "+" or "-" between them results in 0.

How many ways.

1+51-(2+49)+3+48-(4+47)+5+46-(6+45)+24+27-(25+26) 0 can be dismantled in pairs.

The specific way is actually 1 kind, and you can also change the addition and subtraction method that is not used to subtract, and the logic itself is still the same.

There is no 511 + 50 - (2 + 49) + 3 + 48 - (empty shirt 4 + 47) + 5 + 46 - (6 + 45) bucket wide cavity + 24 + 27 - (25 + 26) 0 two by two by a group of clever returns.

I'm sorry, I just wrote it wrong, check it, so you can get it.

How many different ways are there to do this.

My dear, there is only 1 such way ha.