Question

Calculați următoarele sume :
a) 4 + 8 + 12 + 16+...+48+52.
b) 2+4+6+8+...+100.
c) 6+12+18+24+...+666.​

Answer 1

$a) \: \: 4 + 8 + ... + 52 = 4(1 + 2 + ... + 13) = 4 \times \frac{13 \times 14}{2} = 2 \times 13 \times 14 = 364$

$b) \: \: 2 + 4 + ... + 100 = 2(1 + 2 + ... + 50) = 2 \times \frac{50 \times 51}{2} = 50 \times 51= 2550$

$c) \: \: 6 + 12 + ... + 666 = 6(1 + 2 + ... + 111) = 6 \times \frac{111 \times 112}{2} = 3 \times 111 \times 112 = 333 \times 112 = 37296$