Question

Aratati ca numarul 9.(5+10+15+...+200):41 este patrat perfect

Answer 1

[tex]Dam~factor~comun~pe~5:\\ 9*5(1+2+3+...+40):41\\ Avem~o~suma~Gauss~aplicam~formula[n(n+1)]:2\\ =\ \textgreater \ 45(20*41):41=\ \textgreater \ 900\\ a)900~se~termina~in~0=\ \textgreater \ patrat~perfect\\ b) \sqrt{900} =30=\ \textgreater \ patrat~perfect.[/tex]

Answer 2

9x(5+10....+200):41=
avem 40 termeni
9x(40x205:2):41=
9x4100:41=
36900:41=900
√900=30 patrat perfect