Question

Tính

A=1+\(\frac{1}{2}+\frac{1}{^{2^2}}+\frac{1}{2^3}+.....+\frac{1}{2^{2012}}\)

Answer 1

A=1+1/2+1/2^2+...+1/2^2012

2A=2(1+1/2+1/2^2+...+1/2^2012

2A=2+1+1/2+1/2^2+...+1/2^2011

2A-A=2+[(1+1/2+1/2^2+...+1/2^2011)-(1+1/2+1/2^2+...+1/2^2011)]-1/2^2012 (mình làm tắt 1 bước)

A=2-1/2^2012 ! CÒN LẠI TỰ TÍNH

Answer 2

A=\(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\)

2A=\(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\)

2A-A=A=\(\left(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\right)\)

A=\(2-\frac{1}{2^{2012}}\)