A = 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/512 + 1/1024
A x 2 = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/512
A x 2 - A = 1 + 1/2 - 1/2+ 1/4 -1/4 + 1/8 -1/8 + 1/16 -1/16 + ... + 1/512 - 1/512 - 1/1024
A = 1 - 1/1024
A = 1023/1024
A = \(\frac{1}{2}\) + \(\frac{1}{4}\) +\(\frac{1}{8}\)+ \(\frac{1}{16}\)+.....
= (1 - \(\frac{1}{2}\)) + (\(\frac{1}{2}-\frac{1}{4}\) ) + (\(\frac{1}{4}-\frac{1}{8}\)) + ... + (\(\frac{1}{512}\) - \(\frac{1}{1024}\)).
= 1 - \(\frac{1}{1024}\)
= \(\frac{1023}{1024}\)
ĐS 1023/1024
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2^{10}}\)
\(=\frac{1}{^2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)
\(\frac{1}{2}A=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{11}}\)
\(\frac{1}{2}A=A-\frac{1}{2}A=\frac{1}{2^{11}}-\frac{1}{2}\)
\(A=\left(\frac{1}{2^{11}}-\frac{1}{2}\right):\frac{1}{2}=\left(\frac{1}{2^{11}}-\frac{1}{2}\right)\times2=\frac{2}{2^{11}}-\frac{2}{2}=\frac{1}{2^{10}}-1\)
