Question

[BTS]

A= 1/2+1/2^2 + 1/2^3 +...+1/2^2015 +1/2^2016

Giup voi to cgi co dung 10 ngay thui

Answer 1

[Nguyễn Anh Quân]

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

Answer 2

[Đỗ Ngọc Hải]

\(\frac{1}{2}A=\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2014}}\)
\(\Rightarrow A-\frac{1}{2}A=\frac{1}{2}-\frac{1}{2^{2017}}\)
\(\Leftrightarrow A=1-\frac{1}{2^{2016}}\)