Question

demonstrati ca numarul 41(1+2+3+....81) este un patrat perfect

Answer 1

Răspuns:

41(1+2+3+....81)=41·(81·82)/2=41·3321=136161=369² → pp

√136161=369

Answer 2

$\it 41\cdot(1+2+3+\ ...\ +81)=41\cdot\dfrac{81\cdot82}{2}=41\cdot81\cdot41=41^2\cdot9^2=\\ \\ \\ =(41\cdot9)^2=369^2$