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Sa se arate ca 1+3+5+..+2005 este patrat perfect

Răspuns :

Se face suma lui gauss si vei obtine 2006x1003supra 2=1003 la a doua =pp
1+3+5+..+2005=1+2+3+4+5+....+2004+2005-2-4-6-...-2004=
=
2005×2006/2-2(1+2+3+...+1002)=
=
2005×1003-2×1002×1003/2=
=2005×1003-1002×1003=
=1003×(2005-1002)=
=1003×1003=
=1003²  deci patrat perfect