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Aflati numarul natural x, astfel incat: 11+12+...+100=5(1000x-1).

Răspuns :

Suma primilor 10 termeni ai sirului =(10*11)/2; suma a 100 termeni=(100*101)/2
(100*101)/2-(10*11)/2= 5(1000x-1)
5050-55=5000x-5 impartim prin 5 ecuatia obtinem 1010-11=1000x-1
1010-11+1=1000x
1000=1000x => x=1000/1000=> x=1

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