Question

[Vũ Thị Phương Anh]

Tính

A=1+1/2+1/2^2+1/2^3+1/2^4+...+1/2^2014

Giúp mình với các bn ơi

Answer 1

[Muôn cảm xúc]

\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.....+\frac{1}{2^{2014}}\)

\(2A=2+1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2013}}\)

\(2A-A=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2013}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2014}}\right)\)

\(A=2+\left(1-1\right)+\left(\frac{1}{2}-\frac{1}{2}\right)+\left(\frac{1}{2^2}-\frac{1}{2^2}\right)+....+\left(\frac{1}{2^{2013}}-\frac{1}{2^{2013}}\right)-\frac{1}{2^{2014}}\)

\(A=2-\frac{1}{2^{2014}}\)

Answer 2

[Tạ Vũ Đăng Khoa]

A=1-1/2^2015