Question

4×((-1+2-3+4-5+6-7...+1000)

Answer 1

Answer:

$4\times \left(\left(-1+2-3+4-5+6-7+1000\right)\right)$

$calculate\: within \: the \:parentheses$

$-1+2=1$

$=1-3+4-5+6-7+1000$

$1-3=-2$

$=-2+4-5+6-7+1000$

$-2+4=2$

$=-3+6-7+1000$

$3-7+1000$

$=-4+1000$

$=996$

$Multiply:-$

$4\times996$

$=3984$

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Hope it helps..

Have a great day!!

Answer 2

-1 + 2 - 3 + 4 - 5 + 6 - … - 999 + 1000

= -(1 + 3 + 5 + … + 999) + (2 + 4 + 6 + … + 1000)

= -((2 - 1) + (4 - 1) + (6 - 1) + … + (1000 - 1)) + 2 (1 + 2 + 3 + … + 500)

= -((2 + 4 + 6 + … + 1000) - 500) + 2 (1 + 2 + 3 + … + 500)

= -(2 (1 + 2 + 3 + … + 500) - 500) + 2 (1 + 2 + 3 + … + 500)

Let S = 1 + 2 + 3 + … + 500. Then this sum is equal to

= -(2S - 500) + 2S

= -2S + 500 + 2S

= 500

and multiplying by 4 gives 2000.