Question

Aratati ca numarul a este patrat perfect si apoi calculati a :
a = (2 + 4 + 6+... + 100) - 50. va rog repede!

Answer 1

$a = (2 + 4 + 6 + ... + 100) - 50 \\ = 2 \times (1 + 2 + 3 + ... + 50) - 50 \\ = 2 \times \frac{50 \times 51}{2} - 50 \\ = 50 \times 51 - 50 \\ = 50 \times (51 - 1) \\ = 50 \times 50 \\ = {50}^{2}$

Answer 2

Răspuns:

Salutare!

a=(2+4+6+...+100)-50

a=2(1+2+3+..+50)-50

a=2(50•51/2)-50

a=2(2550/2)-50

a=2•1275-50

a=2550-50

a=2500

a²=2500 ==> a=50