Question

Tính tổng sau:

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

Answer 1

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

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

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

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

Answer 2

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

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

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

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

Answer 3

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

Answer 4

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

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

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

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