1)
1 + 2 + 3 + ............ + 80 = 3 240
= 80 × ( 1 + 80 ) / 2 = → aplic formula sumei lui Gauss
= 40 × 81 =
= 3 240
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2)
1 + 2 + 3 + .............. + 100 = 5 050
= 100 × ( 1 + 100 ) / 2 =
= 50 × 101 =
= 5 050
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3)
1 + 2 + 3 + .......... + 90 = 4 095
= 90 × ( 1 + 90 ) / 2 =
= 45 × 91 =
= 4 095
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4)
1 + 2 + 3 + ......... + 68 = 2 346
= 68 × ( 1 + 68 ) / 2 =
= 34 × 69 =
= 2 346
sau:
S₁ = 1 + 2 + 3 + ....... + 68
S₂ = 68 + 67 + 66 + .....+ 1
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2 x S = ( 1 + 68 ) + ( 2 + 67 ) + ( 3 + 66 ) + ......... + ( 68 + 1 )
2 x S = 69 + 69 + 69 + ........ + 69
2 x S = 68 x 69 l : 2
S = 34 x 69
S = 2 346