Question

Exercitiul 5 am nevoie urgent de tot dau coroană ​

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

Răspuns:

- 2011

Explicație pas cu pas:

${2010}^{20} - 2011 \cdot {2010}^{19} + 2011 \cdot {2010}^{18} - 2011 \cdot {2010}^{17} + ... + 2011 \cdot {2010}^{2} - 2011 \cdot 2010 - 1 =$

$= {2010}^{19} \cdot (2010 - 2011) + 2011 \cdot {2010}^{18} - 2011 \cdot {2010}^{17} + ... + 2011 \cdot {2010}^{2} - 2011 \cdot 2010 - 1$

$= - {2010}^{19} + 2011 \cdot {2010}^{18} - 2011 \cdot {2010}^{17} + ... + 2011 \cdot {2010}^{2} - 2011 \cdot 2010 - 1$

$= {2010}^{18} \cdot (- 2010 + 2011) - 2011 \cdot {2010}^{17} + ... + 2011 \cdot {2010}^{2} - 2011 \cdot 2010 - 1$

$= {2010}^{18} - 2011 \cdot {2010}^{17} + ... + 2011 \cdot {2010}^{2} - 2011 \cdot 2010 - 1$

$= {2010}^{17} \cdot (2010 - 2011) + ... + 2011 \cdot {2010}^{2} - 2011 \cdot 2010 - 1$

$= - {2010}^{17} + ... + 2011 \cdot {2010}^{2} - 2011 \cdot 2010 - 1$

...

$= - {2010}^{3} + 2011 \cdot {2010}^{2} - 2011 \cdot 2010 - 1$

$= {2010}^{2} \cdot (- 2010 + 2011) - 2011 \cdot 2010 - 1$

$= {2010}^{2} - 2011 \cdot 2010 - 1$

$= 2010 \cdot (2010 - 2011) - 1$

$= - 2010 - 1 = \bf - 2011$