Question

\(\frac{1}{2}\)\(+\)\(\frac{1}{4}\)\(+\)\(\frac{1}{8}\)\(+\)\(\frac{1}{16}\)...\(+\)\(\frac{1}{2048}\)

Answer 1

\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+..+\frac{1}{2048}\)

\(=1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+..+\frac{1}{2048}\)

\(=1-\frac{1}{2048}\)

\(=\frac{2047}{2048}\)

Answer 2

2047/2048 nha bạn

Answer 3

Ta có:
1/2 = 1 - 1/2
1/4 = 1/2 - 1/4
1/8 = 1/4 - 1/8
…
1/2048 = 1/1024 - 1/2048
Suy ra:
1/2 + 1/4 + 1/8 + ... + 1/2048
= 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + ... - 1/1024 + 1/1024 - 1/2048
= 1 - 1/2048
= 2047/2048

k mình nha

Answer 4

Ta có: 2A=1+ 1/2+1/4+...+1/024

2A-A=1-1/2048

=2047/2048