Question

Calculati in doua moduri: (2+4+6+............+2000)-(1+3+5+............+1999).
(Suma lui Gauss)

Answer 1

(2+4+6+........+2000)-(1+3+5+....+1999)=
=2(1+2+3+...+1000)-[1000*1+2(1+2+3+....+998)]
=2*1000*1001:2-(1000+2*998*999:2)
=1000*1001-(1000+998*999)
=1 001 000-(1000+997 002)
=1 001 000-998 002
=2998
Daca nu ai inteles,spune-mi,te rog!