Răspuns:
Explicație pas cu pas:
( 2+4+6+8+......+100) - ( 1+3+5+7+....+99) =
= 2 × (1+2+3+4+.....+50) - { [ ( 99-1):2+1] × (1 +99):2} =
→ aplic formula sumei lui Gauss
= 2 × 50 × 51 : 2 - ( 50 × 100 : 2 ) =
= 50 × 51 - 50 × 50 =
= 50 × (51-50) =
= 50 × 1 =
= 50 → primul mod
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Al doilea mod:
2+4+6+8+......+100 - => 50 termeni
1+3+5+7+......,+99 => ( 99-1):2+1 = 49+1=50 termeni
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= ( 2 - 1 ) + ( 4-3) + ( 6-5) + ( 8-7) + ....... + ( 100 -99) =
= 1 + 1 + 1 + 1 + 1 + ........... + 1 → de 50 de ori : 2×(1+2+3+.....+50)
= 50 × 1 =
= 50
