A = 2015 - 2015x + 2015x2 - 2015x3 + 2015x4 - 2015x5 +.....+ 2015x2015
A = 2015.(1-x+x2-x3+x4-x5+...+x2015)
Thay x = 2014 và đặt
B = 1-2014+20142-20143+20144-20145+...+20142015
2014B = 2014-20142+20143-20144+20155-20146+...+20142016
2015B = 2014B + B = 1 + 20142016
=> B = \(\frac{1+2014^{2016}}{2015}\)
=> A = 2015.\(\frac{1+2014^{2016}}{2015}\)
=> A = 1+ 20142016