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La suma mas grande es 1000 pues
planteas la ecuacion
x+x+1+x+2+x+3+x+4=1000
5x+10=1000
5x=1000-10
5x=990
x=990/5
x=198
y los numeros serian
numero 1=x=>198
numero 2=x+1=>199
numero 3=x+2=>200
numero 4=x+3=>201
numero 5=x+4=>202
espero ayude