\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2015}}+\frac{1}{2^{2016}}\)

\(\Rightarrow\)\(2A=1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2014}}+\frac{1}{2^{2015}}\)

\(\Rightarrow\)\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2014}}+\frac{1}{2^{2015}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2016}}\right)\)

\(\Rightarrow\)\(A=1-\frac{1}{2^{2016}}\)

           \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2015}}+\frac{1}{2^{2016}}\)

\(\Leftrightarrow\)\(2A=1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2014}}+\frac{1}{2^{2015}}\)

\(\Leftrightarrow\)\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2015}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2016}}\right)\)

\(\Leftrightarrow\)\(A=1-\frac{1}{2^{2016}}\)

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

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

\(2A-A=\left(1+\frac{1}{2}+.....+\frac{1}{2^{2015}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+.....+\frac{1}{2^{2016}}\right)\)

\(A=1-\frac{1}{2^{2016}}\)

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

2A -A= (1+1/2+1/2^2+...+1/2^2015)-(1/2+1/2^2+...+1/2^2016)

A= 1-\(\frac{1}{2^{2016}}\)

Đáp số: A=1-\(\frac{1}{2^{2016}}\)

A=1/2+1/2^2+1/2^3+...+1/2^2016     (1)

2A=1+1/2+1/2^2+...+1/2^2015         (2)

Lấy (2)-(1) được:

A=1+1/2+1/2^2+...+1/2^2015-(1/2+1/2^2+1/2^3+...+1/2^2016)

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

A=1-1/2^2016

Vậy A=1-1/2^2016

viết lại đề cho rõ phân số đi bn

\(A=\left[1+\left(-2\right)\right]+\left[3+\left(-4\right)\right]+....+\left[2013+\left(-2014\right)+2015\right]\)

\(A=\left(-1\right)+\left(-1\right)+....+\left(-1\right)+2015\left(\text{1007 số hạng }\left(-1\right)\right)=1008\)

\(B=\left(-2\right)+4+\left(-6\right)+8+\left(-10\right)+,...+\left(-2014\right)+2016\)

\(B=2+2+....+2\left(\text{504 số hạng 2}\right)=1008\)

c) 1 + ( -3 ) +5 + ( -7 ) + ...........+ 2013 + ( -2015 )

[ 1 + (-3 ) ] + [ 5 + -7 ] + .......... + [ 2013 + ( - 2015 ) ]

 có số cặp là : [ ( 2015 - 1 ) : 2 + 1 ] : 2 = 504 ( cặp )

= -2 + -2 + -2 +..........+ -2

= -2 x 504

= -1008

sai đề là cái chắc

ko chép đúng đề mà

bảo chép đúng rồi mà

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

\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2015}}+\frac{1}{2^{2016}}\)

\(2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2014}}+\frac{1}{2^{2015}}\)

\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2014}}+\frac{1}{2^{2015}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2015}}+\frac{1}{2^{2016}}\right)\)

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

\(A=1-\frac{1}{2^{2016}}\)