Răspuns:
Explicație pas cu pas:
1)
1+3+5+.......+55 = 784
- Aflăm câți termeni impari are suma:
(55-1) : 2 + 1 = 54:2+1 = 28 termeni impari
= 28 × (1+55) : 2 =
= 28 × 56 : 2 =
= 28 × 28 =
= 784
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2.
1+3+5+......+117 = 3 481
(117-1) : 2+1 = 116 : 2 + 1 = 59 termeni sau (117+1):2 = 118:2=59
= 59×(1+117):2 =
= 59×59 =
= 3 481
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3.
1+3+5+.....+201 =10 201
(201-1):2+1=200:2+1=101 termeni impari are suma
= (201+1):2 × (1+201) : 2 =
= 101 × 101 =
= 10 201
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4.
1+3+5+.......+333 = 27 889
= (333+1):2 ×(1+333) : 2 =
= 334:2 × (334 : 2)
= 167 × 167 =
= 27 889
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5.
1+3+5+.......+803 = 161 604
(803-1):2+1 = 802 : 2 + 1 = 402 termeni impari are suma
= 402 × (1+803) : 2 =
= 402 ×804 : 2 =
= 402²=
= 161 604
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6.
1+3+5+........+ 1 111 = 309 136
= (1111+1) : 2 × (1+1111):2 =
= 556 × 1112 : 2 =
= 556 × 556 =
= 309 136
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7.
1+3+5+......+1437 = 516 961
(1437-1) : 2 + 1 = 1436:2+1 = 718+1=719 termeni impari are suma
= 719 ×(1+1437) : 2 =
= 719 × 1 438 : 2 =
= 719 × 719 =
= 516 961
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8.
1+3+5+........+921 =212 521
→ adaug și numerele pare pe care le scad apoi
= 1+2+3+4+....+....+920+921 - (2+4+6+.....+920) =
→ aplic formula sumei lui Gauss
= 921 × (1+921) : 2 - 2 × (1+2+3+....+460) =
= 921 × 922 : 2 - 2 × 460 × 461 : 2 =
= 921 × 461 - 460 × 461 =
= 461 × (921 - 460) =
= 461 × 461 =
= 212 521
