sumele lui gauss
57+58+...+159
8+9+...+20
88+89+...+400
Răspunsuri la întrebare
Răspuns:
Explicație pas cu pas:
57 + 58 + ...... + 159 =11124
159 - 57 + 1 = 103 termeni are suma
= 103 × ( 57 + 159) : 2 =
= 103 × 216 : 2 =
= 103 × 108 =
= 11124
sau:
(1+2+3+.....+56) +57+58+.....+159 - (1+2+3+......+56) =
= 159 × (1+159) : 2 - 56 × (1+56) : 2 =
= 159 × 160 : 2 - 56 × 57 : 2 =
= 25 440 : 2 - 3 192 : 2 =
= 12 720 - 1 596 =
= 11 124
___________________________
8 + 9 + ..... + 20 = 182
20 - 8 + 1 = 13 termeni are suma
= 13 × (8+20) : 2 =
= 13 × 28 : 2 =
= 13 × 14 =
= 182
sau adaug suma primelor 7 numere, apoi o scad:
(1+2+3+....+7)+8+9+....+20 - (1+2+3+....+7) =
= 20 × ( 1+20) : 2 - 7 × ( 1+7) : 2 =
= 10 × 21 - 7 × 8 : 2 =
= 210 - 28 =
= 182
_______________________
88 + 89 + ...... + 400 =
400 - 88 + 1 = 312 + 1 = 313 termeni are suma
= 313 × ( 88 + 400) : 2 =
= 313 × 488 : 2 =
= 152 744 : 2 =
= 76 372
sau:
(1+2+3 + ......+ 87) + 88+89+.....+400 - (1+2+3+.....+87) =
= 400 × (1+400) : 2 - 87 × (1+87) : 2 =
= 400 × 401 : 2 - 87 × 88 : 2 =
= 160 400 : 2 - 7656 : 2 =
= 80 200 - 3828 =
= 76 372