Question

So Sánh : \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2011}}\) với \(1-\frac{1}{2^{2010}}\)

Answer 1

Đặt \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2011}}\)

\(2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2010}}\)

\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2010}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\right)\)

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

Vì \(1-\frac{1}{2^{2011}}< 1-\frac{1}{2^{2010}}\)nên A < \(1-\frac{1}{2^{2010}}\)

Ủng hộ mk nha !!! ^_^

Answer 2

cho mk một tk đi bà con ơi

ủng hộ mk đi làm ơn