[ Toán 9] Casio

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transformers123

$2012^{2014} + 318126$

$=2012^{2014}-1+318127$

$=(2012-1)( 1 + 2012 + 2012^2 + 2012^3 + …. + 2012^{2013})+318127$

Dẫ thấy $(2012-1)( 1 + 2012 + 2012^2 + 2012^3 + …. + 2012^{2013})\ \vdots\ ( 1 + 2012 + 2012^2 + 2012^3 + …. + 2012^{2013})$

Nên: $\dfrac{(2012-1)( 1 + 2012 + 2012^2 + 2012^3 + …. + 2012^{2013})}{318127}$ bằng $2011$ và dư $318127$
 
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