Có : 2A = 1 + 1/2 + 1/2^2 +.....+ 1/2^2015
A = 2A - A = (1+1/2+1/2^2+.....+1/2^2015)-(1/2+1/2^2+.....+1/2^2016)
= 1 - 1/2^2016
Tk mk nha
\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2015}}+\frac{1}{2^{2016}}\)
\(2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2014}}+\frac{1}{2^{2015}}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2014}}+\frac{1}{2^{2015}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2015}}+\frac{1}{2^{2016}}\right)\)
\(A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2015}}+\frac{1}{2^{2016}}-\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^{2015}}-\frac{1}{2^{2016}}\)
\(A=1-\frac{1}{2^{2016}}\)