Question

Cum se face exercitiu a=31+2+4+6+...+60

Answer 1

a = 31 + 2 + 4 + 6 + ....... + 60

a = 31 + 2 × ( 1 + 2 + 3 + ...... + 30 )

a = 31 + 2 × 30 x ( 1 + 30 ) / 2

a = 31 + 30 × 31

a = 31 + 930

a = 961

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2 + 4 + 6 + ....... + 60 = 2 × 1 + 2 × 2 + 2 × 3 + 2 × 4 + ........ + 2 × 30

→ am dat factor comun pe 2

= 2 × ( 1 + 2 + 3 + ....... + 30 ) =

→ aplic formula sumei lui Gauss:  nr termeniai sumei × (primul termen + ultimul ) totul supra 2

= 2 × 30 ( termeni ) × ( 1 + 30 ) / 2

→ simplific pe 2 cu 2 si ramane : 30 × 31