\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{2048}\)
\(=1-\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2048}\)
\(=1-\frac{1}{2048}\)
\(=\frac{2047}{2048}\)
NHận xét :
1/2 = 1 - 1/2
1/4 = 1/2 - 1/4
1/8 = 1/4 - 1/8
...................
1/2048 = 1/1024 - 1/2048
Vậy 1/2 + 1/4 + 1/8 + ... + 1/2048
= 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + ... - ... + 1/1024 - 1/2048
= 1 - 1/2048 = 2047/2048