Question

A) 1+2+3+..........+21
B) 1+2+3+..........+53
C) 7+8+9+10....... +42
D) 17+18+19.....+99
❗Urgent va rog (dau coroana) ❗​

Answer 1

Răspuns:

Explicație pas cu pas:

a)  1 + 2 + 3 + ......+21 = 21 × (1+21) : 2 = 21 × 22 : 2 = 462 : 2 = 231

→ aplic formula sumei lui Gauss:

= nr. termeni × ( primul + ultimul termen) : 2

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b)   1+2+3+.......+53 = 53 × ( 1+53) : 2 = 53×54 : 2 = 2862 : 2 = 1432

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c) 7+8+9+10+.....+42 =

42 - 7 + 1 = 36 termeni are suma

= 36 × ( 7+42) : 2 =

= 36 × 49 : 2 =

= 1764 : 2 =

= 882

• sau adaug primele 6 numere naturale nenule, apoi le scad:

1+2+3+4+5+6+7+8+9+.....+42 - 1 - 2 - 3 - 4 - 5 - 6 =

= 42×(1+42) : 2 - (1+2+3+4+5+6) =

= 42×43 : 2 - 6×7 : 2 =

= 1806 : 2 - 42 : 2 =

= 903 - 21 =

= 882

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d)   17 + 18 + 19 + ....... + 99 =

99 - 17 + 1 = 82 + 1 = 83

= 83 × ( 17+99) : 2 =

= 83 × 116 : 2

= 9628 : 2 =

= 4814

• sau adaug primele 16 numere naturale nenule, apoi le scad:

1+2+3+......+99 - 1-2-3-4-......-16 =

= 99 × ( 1+99) : 2 - (1+2+3+....+16) =

= 99 × 100 : 2 - 16×(1+16) : 2 =

= 9900 : 2 - 16×17 : 2 =

= 4950 - 136 =

= 4814

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