Question

calculati
a) 1-2+3-4+5-6+...+2017-2018=
ajutor !!!

Answer 1

Sper ca te.am ajutat

Answer 2

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