Question

what is the value of -1+2-3+4-5+6-4+....+1000? ​

Answer 1

There should be -7 after +6, I believe.

$-1+2-3+4-5+6-7+\ldots+1000=\\-(1+3+5+\ldots+999)+2+4+6+\ldots+1000=\\-(1+999+3+997+\ldots+499+501)+2+1000+4+998+\ldots+500+502=\\-250\cdot1000+251\cdot1002=\\-250000+250500=\\500$