Question

[Linh vk Jimin]

Tính giá trị của biểu thức

x^2016 + x^2015+ x^2014+...+x+1 tại x =2

Answer 1

[Trần Thanh Phương]

\(A=1+2+...+2^{2015}+2^{2016}\)

\(2A=2+2^2+...+2^{2016}+2^{2017}\)

\(2A-A=\left(2+2^2+...+2^{2017}\right)-\left(1+2+...+2^{2016}\right)\)

\(A=2^{2017}-1\)

Answer 2

[X1]

\(B=2^{2016}+2^{2015}+2^{2014}+...+2+1\)

\(\Rightarrow B=1+2+...+2^{2014}+2^{2015}+2^{2016}\)

\(\Rightarrow2B=2+2^2+...+2^{2015}+2^{2016}+2^{2017}\)

\(\Rightarrow2B-B=2^{2017}-1\Rightarrow B=2^{2017}-1\)