Question

[đô rê mon]

-1-1/2-1/4-1/8-1/8-...-1/1024

Answer 1

[Minh Anh]

\(A=-1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-...-\frac{1}{1024}\) 

\(A=-\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)\)

\(A=-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)\)

\(2A=-\left(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)\)

\(2A-A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}-2-1-\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^9}\)

\(A=-2+\frac{1}{2^{10}}\)

Answer 2

[l҉o҉n҉g҉ d҉z҉]

Ta có: -1 - 1/2 - 1/4 - 1/8 - ... -1/1024

= -1 - (1 - 1/2) - (1/2 - 1/4) - .... - (1/512 - 1/1024)

= -1 - (1 - 1/1024)

= -1 - 1023/1024

= -2047/1024