Question

1) 1+2+3+............+80= 2)1+2+3+..............100= 3)1+2+3+..........+90= 4) 1+2+3+.........68= Raspundeti-mi la aceasta intrebare va rog! :)

Answer 1

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