10 + 15 + 20 + ... + 2 010 - 9 - 13 - 17 - ... - 1 609 =
= ( 10 + 15 + 20 + ...... + 2010 ) - ( 9 + 13 + 17 + ....... + 1 609 ) =
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10 + 15 + 20 + ...... + 2010 =
→ stabilesc cati termeni are suma cu ratia 5
( 2010 - 10 ) : 5 + 1 = 2 000 : 5 + 1 = 400 + 1 = 401 termeni are suma
→ aplic formula sumei lui Gauss
= 401 × ( 10 + 2 010 ) / 2 =
= 401 × 2 020 / 2 =
= 401 × 1010 =
= 405 010
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9 + 13 + 17 + ....... + 1 609 =
→ stabilesc cati termeni are suma cu ratia 4
( 1 609 - 9 ) : 4 + 1 = 1 600 : 4 + 1 = 401 termeni are suma
= 401 × ( 9 + 1 609 ) / 2 =
= 401 × 1 618 / 2 =
= 401 × 809 =
= 324 409
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= ( 10 + 15 + 20 + ...... + 2010 ) - ( 9 + 13 + 17 + ....... + 1 609 ) =
= 401 × 1010 - 401 × 809 = 405 010 - 324 409 = 80 601
sau dau factor comun pe 401:
= 401 × ( 1010 - 809 ) =
= 401 × 201 =
= 80 601
