Question

DAU 30 PUNCTE SI COROANA

d) 1+2+3+.....+124;

g) 5+6+7+.....+81;

h) 1+2+3+.....+512​

Answer 1

$d) \: \: \: 1 + 2 + 3 + ... + 124 \\ \\ = \frac{124 \times (124 + 1)}{2} \\ \\ = 62 \times 125 \\ = 7.750 \\ \\ \\ \\ \\ g) \: \: \: 5 + 6 + 7 + ... + 81 = \\ = (1 + 2 + 3 + ... + 81) - (1 + 2 + .. + 4) \\ \\ = \frac{81 \times (81 + 1)}{2} - \frac{4 \times (4 + 1)}{2} \\ \\ = 81 \times 41 - 2 \times 5 \\ = 3321 - 10 \\ = 3.311 \\ \\ \\ \\ \\ h) \: \: \: 1 + 2 + 3 + ... + 512 \\ \\ = \frac{512 \times (512 + 1)}{2} \\ \\ = 256 \times 513 \\ = 131.328$