Question

1) S=2+4+6+.........+324
2)S=3+6+9+.........+324
3)S=4+8+12+........+324
4)S=5+10+15+.......+324
5)S=13+16+19+......+94
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Answer 1

Răspuns:

Explicație pas cu pas:

1) S=2+4+6+.........+324

S = 2×1+2×2+2×3+......+2×162

S = 2×(1+2+3+........+162)

S = 2×162×(1+162) : 2

S = 162 × 163

S = 26 406

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2)S=3+6+9+.........+324

S = 3×1+3×2+3×3+......+3×108

S = 3× (1+2+3+.......+108)

S = 3×108 ×(1+108) : 2

S = 3×54×109

S = 17 658

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3)S=4+8+12+........+324

S = 4×1+4×2+4×3+....+4×81

S = 4×(1+2+3+.....+81)

S = 4× 81 × (1+81) : 2

S = 2 × 81 × 82

S = 162 × 82

S = 13 284

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4)S=5+10+15+.......+324

                               324 = 320 + 4 = (5×64) + 4

S = 5×1+5×2+5×3+....+5×64 + 4

S = 5 × (1+2+3+4+.......+64) +  4

S = 5 × 64 × (1+64) : 2 + 4

S = 320 × 65 : 2 + 4

S = 10 400 + 4

S = 10 404

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5)S=13+16+19+......+94

(94 - 13) : 3 + 1 = 81 : 3 + 1 = 27+1 = 28 termeni are suma

S = 28 × ( 13+94) : 2

S = 28 × 107 : 2

S = 1 498