Răspuns: - 1009
Explicație pas cu pas:
a) 1 - 2 + 3 - 4 + 5 - 6 + ...... + 2017 - 2018 =
= ( 1 + 3 + 5 + ..... + 2017 ) - 2 × ( 1 + 2 + 3 + ...... + 1009 ) =
= ( 1009 × 2018 : 2 ) - 2 × ( 1009 × 1010 ) : 2 =
= ( 1009 × 1009 ) - ( 1009 × 1010 ) =
= 1009 × ( 1009 - 1010 ) =
= - 1009
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1 + 3 + 5 + ..... + 2017 =
→ stabilesc cati termeni are suma numerelor impare consecutive
( 2017 - 1 ) : 2 + 1 = 2016 : 2 + 1 = 1008 + 1 = 1009 termeni
→ aplic formula sumei lui Gauss
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- 2 - 4 - 6 - ......- 2018 =
= - 2 × ( 1 + 2 + 3 + ..... + 1009 )
→ il dau factor comun pe - 2
