Question

calculeaza prin metoda lui gauss
1+3+5+.....+139=

6+11+16+...+2006=

Answer 1

1+3+5+.....+139=
=1+2+3+4+5+6+.....+138+139-2-4-6-....-138=
=139×140/2-2(1+2+3+....+69)=
=139×70-2×69×70/2=
=70×(139-69)=
=70×70=70²=4900

 6+11+16+...+2006=
=6+(6+5)+(6+10)+...+(6+2000)=
pasul 11-6=5
nr termeni (2006-6):5+1=400+1=401
=6×401+5+10+...+2000=
=2406+5×400×401/2=
=2406+5×200×401=
=2406+1000×401=
=2406+401000=403406