Question

Aratati ca numarul egal 2plus4plus6plus ...plus100plus 51 este patrat perfect​

Answer 1

Răspuns:

a = 2 + 4 + 6 + .. + 100+51

a = 2(1+2 + ... +50)+51

a = 2·50·51 : 2+51

a = 50·51+51

a = 51(50+1)

a = 51·51 =51 ²→ patrat perfect

Answer 2

Răspuns: Ai demonstrația mai jos

Explicație pas cu pas:

$\bf n = 2 + 4 + 5 +........+100 +51$

$\bf n = 2\cdot \big(1+2+3+4+...+50\big) +51$

$\bf n = 2\cdot \big(50\cdot51:2\big) +51$

$\bf n = 2\cdot 25\cdot51 +51$

$\bf n = 50\cdot51 +51$

$\bf n = 51\cdot\big(50 +1\big)$

$\bf n = 51\cdot51$

$\red{\boxed{\bf n = 51^{2} \longrightarrow patrat ~perfect }}$