\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{2048}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-...-\frac{1}{2048}+\frac{1}{2048}\)
\(=1-\frac{1}{2048}\)
\(=\frac{2047}{2048}\)
k mk nha
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 ^_^
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