Question

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

Answer 1

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

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

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

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

k mk nha

Answer 2

Đặt A = 1/2¹ + 1/2² + 1/2³ + 1/2⁴ +... +1/2¹¹

 2A = (1/2¹ + 1/2² + 1/2³ + 1/2⁴ +... +1/2¹¹⁾.2

2A =  1 + 1/2 +1/2² + ...+ 1/2¹⁰

2A - A = ( 1 + 1/2 +1/2² + ...+ 1/2¹⁰ ) -  (1/2¹ + 1/2² + 1/2³ + 1/2⁴ +... +1/2¹¹)

A = 1 - 1/2¹¹

A = 1 - 1/2048

A = 2047/2048

NHA CÁC BẠN ^_^

Answer 3

Đặt S = 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2048 

   2.S = 1 + 1/2 + 1/4 + 1/8 + ... + 1/2048

2.S - S = ( 1 + 1/2 + 1/4 + 1/8 + ... + 1/2048 ) - ( 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2048 )

      S  =  1 - 1/2048

       S =       2047/2048     

Answer 4

2047/2048 nha

k mk nha