Question

A=1+1/2+1/2²+1/2³+1/2⁴⁺...+1/2²⁰¹⁷

^{Rút gọn}

Answer 1

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

\(2A-A=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2016}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{2017}}\right)\)

\(A=2-\frac{1}{2^{2017}}\)

Answer 2

A=1+1/2+1/2²+1/2³+...+1/2²⁰¹⁷ 

1/2A=1/2+1/2²+1/2³+1/2⁴+...+1/2²⁰¹⁸

A-1/2A=(1+1/2+1/2²+1/2³+...+1/2²⁰¹⁷)-(1/2+1/2²+1/2³+1/2⁴+...+1/2²⁰¹⁸)

A-1/2A=1-2^2012018

1/2A=1-1/2²⁰¹⁸

A=(1-1/2²⁰¹⁸).2

A=2-2²⁰¹⁹