Question

Calculați 3+5+7+...+2001-2-4-6-2000

Answer 1

3 + 5 + 7 + ... + 2 001 - 2 - 4 - 6 - 2 000 = 1 000

= 3 + 5 + 7 + ... + 2 001 - 2 ( 1 + 2 + 3 + ...... + 1000 ) =

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3 + 5 + 7 +  ....... + 2 001 =

→ stabilesc cati termeni are suma  cu ratia 2

( 2 001 - 3 ) : 2 + 1 = 1 998 : 2 + 1 = 999 + 1 = 1 000 termeni

→ aplic formula sumei lui Gauss

= 1 000 × ( 3 + 2 001 ) / 2 =

= 500 × 2 004 =

= 1 002 000

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= ( 3 + 5 + 7 + ... + 2 001 )  - 2 ( 1 + 2 + 3 + ...... + 1000 ) =

=  1 002 000 - 2 × 1 000 × 1001 / 2 =

= 1 002 000 - 1 001 000 =

=  1 000