Question

-1 - \(\dfrac{1}{2}\)- \(\dfrac{1}{4}\)-.....- \(\dfrac{1}{1024}\)

Answer 1

 

Đặt \(B=1+\dfrac{1}{2}+...+\dfrac{1}{1024}\) và \(A=-1-\dfrac{1}{2}-\dfrac{1}{4}-...-\dfrac{1}{1024}\)

=>A=-B

\(B=1+\dfrac{1}{2}+...+\dfrac{1}{1024}\)

=>\(\dfrac{1}{2}B=\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{2^{11}}\)

=>\(-\dfrac{1}{2}B=\dfrac{1}{2^{11}}-1\)

=>\(\dfrac{1}{2}B=1-\dfrac{1}{2^{11}}=\dfrac{2^{11}-1}{2^{11}}\)

=>\(B=\dfrac{2^{11}-1}{2^{10}}\)

=>\(A=\dfrac{1-2^{11}}{2^{10}}\)