Question

1+2+3...+16= 1+2+3+...+100= 21+22+...+100= 17+18+...+40helpppp este GAUSS plzzzz am extrem de mult de scris

Answer 1

1 + 2 + 3 + .... + 16 = 16 × ( 1 + 16 ) / 2 = 8 × 17 = 136

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1 + 2 + 3 + ..... + 100 = 5 050

= 100 × ( 1 + 100 ) / 2 =

= 50 × 101 =

= 5 050

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S = 21 + 22 + ..... + 100

→ stabilesc cati termeni are suma, cu ratia 1

100 - 21 + 1 = 79 + 1 = 80 termeni are suma

→ aplic formula sumei lui Gauss

S = 80 × ( 21 + 100 ) / 2

S = 40 × 121

S = 4 840

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17 + 18 + .... + 40 = 684

=  ( 40 - 17 + 1 ) termeni × ( 17 + 40 ) / 2 =

= 24 × 57 / 2 =

= 12 × 57 =

= 684