Question

Calculați următoarele sume : f)15+16+17+....+70; g)5+6+7+....+81; h)1+2+3+....+512; i)317+318+319+....+400

Answer 1

f)
15+16+17+....+70 =
(70 - 15 + 1 = 56 termeni)
= (15+70) × 56 : 2 =
= 85 ×28 =
= 2 380

g)
5+6+7+....+81 =
81 - 5 + 1 = 77 termeni are suma
(5 + 81) × 77 : 2 =
= 86 × 77 : 2 =
= 43 × 77 =
= 3 311

h)
1+2+3+....+512 =
= 512 × (512+ 1) : 2 =
= 512 × 513 : 2 =
= 256 × 513 =
= 131 328

i)
317+318+319+....+400 =
= (1+2+3+...+400) - (1+2+3+...+316) =
= 400×401 : 2 - 316 × 317 : 2 =
= 200 × 401 - 158 × 317 =
= 80 200 - 50 086 =
= 30 114