Being negative

$(1-2+3-4+5..+999)$

$= ((1-2)+(3-4)+...+(999-1000)+1000)$

$= ((-1-1-1-....$ upto $\frac{1000}{2}$ terms or 500 terms) $+1000)$

$= (-500+1000) = \boxed{500}$

The total (addition) of the first "n" odd numbers is "n^2". Then 1 + 3 + 5 + . . . + 999 is "500^2". In the other hand, the total (addition) of the first "n" even numbers is n(n+1). Then 2 + 4 + 6 + . . . + 998 is 499(499+1)=249,500. Therefore, 1 - 2 + 3 - 4 + ... 999 = 250,000 - 249,500 = 500

As We can observe that every doublet(group of two) in this pattern sum up to -1........ So in total we have 1000 integers and so the sum up will be (1000/2)-1................ and now adding that value(-499) to last digit(999) we get 500

1+3+5--------------------------------999 are in arithematic progression so evaluate the sum which comes out to be 250000. similarly 2+4+6------------------------998 are also in AP so evaluate the sum which comes to be 249500 and subtract them

Following the order of operations, we have,

$1 - 2 + 3 - 4 + 5 ...... + 999 = 1 + 1 + 1 ..... + 1$

There will be ( $\frac {998}{2} + 1$ =) $500$ ones.

So the sum will be $500 \times 1 = \boxed {500}$ .

1-2= -1 -1+3= 2 2-4 = -2 -2+5= 3.... The pattern here is:... let the last term= n.... => suppose n is an odd number , the value of the expression= (n+1)/2. .... => If n is an even number, the value of the expression= - (n/2)..... Here n=999..... therefore answer = (999+1)/2..... =500

999+1=1000

1000/2=500

make the group for the numbers [(1-2)+(3-4)+(5-6)+....+(997-998)]+999

there are 998:2 = 499 numbers in the symbol of (...)

each (...) has value of -1

so there amount of (...) is => -1x499 = -499

[(1-2)+(3-4)+(5-6)+....+(997-998)] + 999 =....

[-499] + 999 = 500

Every time you move up two numbers, your answer moves up by one. There are 500 pairs of numbers so that means that the answer is 500

Let the series is S=1-2+3-4+5-6.......+997-998+999

S= 1-2+3-4+5........-996+997-998+999

ADDING THIS TWO: 2S=1-1+1-1.........+1-1+1+999 SO S=500 AS, ALL THE TERMS EXCLUDING LAST AND THE ONE BEFORE LAST CANCELS.

1-2+3-4+5-6+7-8+.....+999=s (1+3+5+7+....+999)-(2+4+6+8+.....+998)=0

Now, 1+3+5+7+....+999=500/2(2.1+(500-1)*2)=250000

again 2+4+6+8+.....+998= 499/2(2.1+(499-1)*2)=249500

So, S=250000-249500= 500

(1-2)+(3-4)+(5-6).........+(997-998)+999 -1+(-1)+(-1)+(-1).....499times +999 =499(-1)+999 =500

The result of every two step is "-1". So, there will be 499 times{(999-1)/2} "-1". Which means -499. The last step will be 999-499, which results 500.

Denote

S = 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... + 999

S1 = 1 + 3 + 5 + 7 + ... + 999 S2 = 2 + 4 + 6 +8 + ... + 998

Note that S1 is the sum of terms of an arithmetic progression with initial term 1 and ratio 2. S2 is the sum of terms of an arithmetic progression with term initial 2 and ratio 2.

S = S1 - S2

Then,

S = 500.

Sum of first two numbers is -1 and the first four numbers is -2 .Let us consider first 998 numbers.Sum of first 998 numbers is 499 times -1 =-499 . Then we do -499+999 =500

OBSERVE FIRST TWO TERMS AND THEN ANOTHER TWO TERMS AND THEN ANOTHER TWO.... WE OBSERVE THAT THE VALUE OF EACH PAIR IS -1. SO FOR FIRST 2 TERMS VALUE IS -1. FOR FIRST 4 TERMS VALUE IS -2. SO FOR FIRST N TERMS VALUE IS -N/2. SO FOR FIRST 998 TERMS VALUE IS -998/2=-499. SO VALUE OF 1-2+3....................+999=-499+999=500. SO ANSWER IS 500.

Each adjacent pair gives a sum of negative one. There are 998/2 pairs from 1 to 998, so that the total sum is -499. Adding this to 999 gives 500.

There are 500 Odd Numbers with 2 sequence each(1+3+5+7+9....+999)=250,000(a) There are 499 even numbers with 2 sequence each(-2-4-5-6-8....-998)=-249,500(b) a+b=250,000+(-249,500)=250,000-249,500=500

1 (-2+3)=1 (-4+5)=1 (-6+7)=1 and so on therefore (-998+999)=1

ANSWER 1+499=500

Sum of first 500 odd numbers (500^2) - Sum of first 499 even numbers (499*500)

the number pattern (1-2) + (3-4) + (5-6) + (7-8) ...... + 999 step 1: -1 + -1 + -1 + -1...... (until 998) = -499

step 2: -499 + 900 = 500

Before number 999 is 998 <=> there is 499 pair number. => 999 - 499 = 500

1+(3+5+7+......+999)-(2+4+6+8+......+998)=1+n(n+2)-n(n+1) & n= 998/2=499, = 1+n n+2n-n n-n =1+n =1+499=500

1^2 + 3^2 +.......+ 997 = 499^2 2^2 + 4^2 +......+ 998 = 499^2 + 499 499^2-(499^2+499) = -499 999-499 = 500

every 2 numbers are equal to -1, then you have to multiply it by 500 because 1000/2 is 500.

1-2 = 3-4 = 5-6 = .... = -1

1-2 + 3-4 +5-6 + .... + 997-998 + 999 =

(-1)*998/2 + 999 = 500