Question

ayuda porfavooor
procedimiento

Answer 1

Respuesta:

12

Explicación paso a paso:

Tenemos:

$(2020^{2} -2019^{2})-(2018^{2}-2017^{2})+(2016^{2}-2015^{2})-(2014^{2}-2013^{2})+(2012^{2}-2011^{2})-(2010^{2}-2009^{2})$

Diferencia de cuadrados:

$a^{2} -b^{2} =(a+b)(a-b)$

Operemos por partes; aplicando la diferencia de cuadrados:

$(2020^{2} -2019^{2})=(2020+2019)(2020-2019)=(4039)(1)=4039$

$(2018^{2}-2017^{2})=(2018+2017)(2018-2017)=(4035)(1)=4035$

$(2016^{2}-2015^{2})=(2016+2015)(2016-2015)=(4031)(1)=4031$

$(2014^{2}-2013^{2})=(2014+2013)(2014-2013)=(4027)(1)=4027$

$(2012^{2}-2011^{2})=(2012+2011)(2012-2011)=(4023)(1)=4023$

$(2010^{2}-2009^{2})=(2010+2009)(2010-2009)=(4019)(1)=4019$

Reemplazamos valores en la situación inicial:

$4039-4035+4031-4027+4023-4019$

Operamos:

$4039-4035+4031-4027+4023-4019$

$4+4031-4027+4023-4019$

$4035-4027+4023-4019$

$8+4023-4019$

$4031-4019$

$12$