Question

(x+3x+5x+.....+2019x)-(2x+4x+6x+.....+2020x)=2020​

Answer 1

Răspuns:

Explicație pas cu pas:

(x+3x+5x+.....+2019x)-(2x+4x+6x+.....+2020x)=2020​

x+3x+5x+.....+2019x+2019x-2019x=2x+4x+6x+......+2020x-2019x

2x+4x+6x+......+2020x-2019x-2x-4x-6x-.........-2020x=2020

-2019x=2020     x=-2020/2019

Answer 2

Răspuns:   x = - 2

Explicație pas cu pas:

( x + 3x + 5 x + ........+ 2019) - ( 2x+4x+6x+......+2020x) = 2020

->  il dau pe x factor comun din prima paranteza, iar pe 2 x din a doua paranteza factor comun

x(1+3+5+........+2019) - 2x(1+2+3+....+1010) = 2020

x × 1010 × 1010 - 2 x × 1010 × (1+1010):2 = 2020

x × 1010² - x × 1010 × 1011 = 2020

->  1010 x factor comun

x × 1010 × ( 1010 - 1011) = 2020

x × 1010 × ( - 1 ) = 2020

x = 2020 : ( - 1010)

x = - 2

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1+3+5+.....+2019 =

(2019 - 1 ) : 2 + 1 = 2018:2+2=1010 termeni are suma numerelor impare

-> aplic formula sumei lui Gauss

= 1010 × ( 1+2019) : 2 =

= 1010 × 2020:2 =

= 1010 × 1010

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2 x ( 1+2+3+.....1010) = 2 x × 1010 × ( 1+1010) : 2

->  aplic formula sumei lui Gauss pentru suma numerelor consecutive, ce incep cu 1:  nr. termeni×(primul +ultimul termen):2

-> 2 /2 = 1