Gọi tổng trên là A
\(\Leftrightarrow A=1+\left(-2\right)+2^2+...+2^{2014}+\left(-2\right)^{2015}\)
\(\Rightarrow2.A=2.1+\left(-2.2\right)+2.2^2+...+\left(-2.2\right)^{2015}\)
\(\Rightarrow2A=2+\left(-2\right)^2+2^3+...+\left(-2\right)^{2016}\)
\(\Leftrightarrow2A=2+2^2+2^3+...+2^{2016}\)
\(\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{2016}\right)-\left[1+\left(-2\right)+2^3+...+\left(-2\right)^{2015}\right]\)\(\Rightarrow A=2^{2016}-1\)
Kho..................wa.....................troi.....................thi......................lanh.................ret.......................ai........................tich..........................ung.....................ho........................minh.....................cho....................do....................lanh
Đặt A = ( - 2 )0 + ( - 2 )1 + ( - 2 )2 + ..... + ( - 2 )2014 + ( - 2 )2015
<=> - 2A = - 2.[ ( - 2 )0 + ( - 2 )1 + ( - 2 )2 + ..... + ( - 2 )2014 + ( - 2 )2015 ]
<=> - 2A = ( - 2 )1 + ( - 2 )2 + ( - 2 )3 + ..... + ( - 2 )2015 + ( - 2 )2016
<=> - 2A - A = [ ( - 2 )1 + ( - 2 )2 + ( - 2 )3 + .... + ( - 2 )2015 + (- 2 )2016 ] - [ ( - 2 )0 + ( - 2 )1 + ( - 2 )2 + ... + ( - 2 )2015 ]
<=> - 3A = ( - 2 )2016 - 1
<=> A = [ ( - 2 )2016 - 1 ] : ( - 3 )
