Question

aflati x care verifica egalitatea 1+3+5+7+......+99+x=2+4+6+8+......+100

Answer 1

1 + 3 + .. + 2n - 1 = n ²

2n - 1 = 99 => 2n = 100 => n = 50

1 + 3 + .. + 99 +x = 2(1 + 2 + .. + 50)

50² + x = 2·50·51 : 2

50² + x = 50·51

2500 + x = 2550

x = 50