Răspuns:
Explicație pas cu pas:
a) 1+2+3+.....+27 =
= 27 × (1+27) : 2 =
= 27×28 : 2 =
= 756 : 2 =
= 378
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b) 13 + 14 + 15 + ...... + 50 =
50-13+1 = 37+1=38 termeni are suma
= 38 × ( 13+50) : 2 =
= 38 × 63 : 2 =
= 2 394 : 2 =
= 1 197
- sau adaug suma primele 12 numere nenule, apoi o scad:
1+2+3+........+50 - (1+2+3+.......+12) =
= 50×(1+50) : 2 - 12×(1+12):2 =
= 50×51 : 2 - 6×13 =
= 2550 : 2 - 78 =
= 1275 - 78 =
= 1 197
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c) 5 + 10 + 15 + ....... + 505 =
= 5×1 + 5×2 + 5×3 + ....... + 5×101 =
- îl dau factor comun pe 5
= 5 × ( 1+2+3+.....+101) =
= 5 × 101 × (1+101) : 2 =
= 505 × 102 : 2 =
= 51 510 : 2 =
= 25 755
