Question

Tính một cách hợp lý : A=\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.....+\frac{1}{2^{2009}}+\frac{1}{2^{2010}}\)

Answer 1

Ta có : 

\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2009}}+\frac{1}{2^{2010}}\)

\(2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2008}}+\frac{1}{2^{2009}}\)

\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2008}}+\frac{1}{2^{2009}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2009}}+\frac{1}{2^{2010}}\right)\)

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

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

Vậy \(A=\frac{2^{2010}-1}{2^{2010}}\)

Chúc bạn học tốt 

Answer 2

Ai nhanh mình k !