Question

4×((-1+2-3+4-5+6-7...+1000)

Answer 1

-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.

Answer 2

`4* \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*996`

`=3984`

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Hope it helps..

Have a great day!!