Question

Aratati ca nr x=1004+2+4+6+...+2006 este patrat perfect si calculati radical din x

Answer 1

consider S=2+4+6+...+ 2004+.2006 si S=2006+2004+......4+2;; adunam cele doua sume 2S=2008+2008+....2008 ( sunt 2006:2=1003 termeni)=> S=2008*1003/2, simplifical si =>S=1004*1003. atunci x=1004+1004*1003=1004(1+1003)=1004*1004=> x= 1004 la patrat, radical din 1004 la patrat= 1004