Question

(x+1)+(x+3)+(x+5)+........+(x+999)=0

 

Answer 1

x . 500+ (1+3+5+....+999)=0

x.500+ 250000=0

x. 500= 0-250000

x . 500 = -250000

x = -250000: 500

x= -500

 

Answer 2

\(x\in\left\{-1;-3;-5;-7;...;-997;-999\right\}\)

Answer 3

[(x+1)+(x+999)]+[(x+3)+(x+997)+...+[(x+499)+(x+501)]=0

(x.2+1+999).225=0

x.2+1000=0:225=0

x.2=0-1000=-1000

x=-1000:2=-500

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