Question

7+9+11+...+2011-6-8-10-...2010=

Answer 1

= ( 7 + 9 + 11 + ... + 2011)  - 2 × ( 3 + 4 + 5 + ...... + 1005 ) =

                                      → am dat factor comun pe - 2

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7 + 9 + 11 + .... + 2011 =

→ stabilesc cati termeni are suma cu ratia 2 ( 9 - 7 = 2;   11 - 9 = 2;.... )

( 2011 - 7 ) : 2 + 1 = 2 004 : 2 + 1 = 1 002 + 1 = 1 003 termeni are suma

→ aplic formula sumei lui Gauss

= 1003 × ( 7 + 2011 ) : 2 =

= 1003 × 2018 : 2 =

= 1003 × 1009 =

= 1 012 027

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2 × ( 3 + 4 + 5 + .... + 1005 ) =

1005 - 3 + 1 = 1003 termeni are suma: 3 + 4 + 5 + .... + 1005

= 2 × 1 003 termeni × 1008 : 2 =

= 1003 × 1008

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= ( 7 + 9 + 11 + ... + 2011)  - 2 × ( 3 + 4 + 5 + ...... + 1005 ) =

= 1003 × 1009 - 1003 × 1008 =

= 1003 × ( 1009 - 1008 )

= 1003 × 1 =

= 1003