Question

comparati urmatoarele sume :S/1.=2+4+6+....+100si S/2=4+8+12+....+200,si apoi calculati 3×S/2-4×S/1 × care este cu S si are in fata linia asta /cu nr este jos sub S de ex asa S/1. 1acela este jos la S

Answer 1

S₁ = 2 + 4 + 6 + ..... + 100

S₁ = 2 x ( 1 + 2 + 3 + ...... + 50 )

S₁ = 2 x [ 50 x ( 1 + 50 ) ] / 2

S₁ = 50 x 51

S₁ = 2 550

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S₂ = 4 + 8 + 12 + ....... + 200

S₂ = 4 x ( 1 + 2 + 3 + ...... + 50 )

S₂ = 4 x [ 50 x ( 1 + 50 ) ] / 2

S₂ = 2 x ( 50 x 51 )

S₂ = 2 x 2 550

S₂ = 5 100

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S₁  <  S₂;    2 550 <   5 100

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3 x S₂ - 4 x S₁ = 3 x 5 100 - 4 x 2 550 = 15 300 - 10 200 = 5 100 → diferenta