Question

Cat e 63+66+69+...+537 dau coroana

Answer 1

63 + 66 + 69 + ... + 537 =

= (60 + 3) + (60 + 6) + .. + (60 + 477)

= 60 + 60 + .. + 60 + 3(1 + 2 + .. + 159)

= 60 x 159 + 3 x 159 x 160 : 2

= 9 540 + 38 160

= 47 700

Answer 2

63 + 66 + 69 + ..... + 537 = 47 700

→ stabilesc cati termeni are suma cu ratia = 3 ( 66 - 63 = 3;   69 - 66 = 3; .... )

( 537 - 63 ) : 3 + 1 = 474 : 3 + 1 = 158 + 1 = 159 termeni are suma

→ aplic formula sumei lui Gauss:

= 159 × ( 63 + 537 ) : 2 =

= 159 × 600 : 2 =

= 159 × 300 =

= 47 700

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sau:

S =  63    + 66 +   69 + ...... + 537

S = 537  + 534 + 531 + ......  +  63

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2 × S = ( 63 + 537 ) + ( 66 + 534 ) + ( 69 + 531 ) + ........... + ( 537 + 63 )

→ aflam cate astfel de sume sunt ( stabilind cati termeni are suma ) :

( 537 - 63 ) : 3 + 1 = 159 termeni are suma

2 × S = 600 × 159 termeni

S = ( 600 × 159 ) : 2

S = 95 400 : 2

S = 47 700