Question

Tính :\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\).

Answer 1

63/64

Answer 2

\(A=\frac{1}{2}+\frac{1}{4}+...........+\frac{1}{64}\)

\(\Leftrightarrow A=\frac{1}{2}+\frac{1}{2^2}+...........+\frac{1}{2^6}\)

\(\Leftrightarrow2A=1+\frac{1}{2}+\frac{1}{2^2}+.........+\frac{1}{2^5}\)

\(\Leftrightarrow2A-A=\left(1+\frac{1}{2}+.........+\frac{1}{2^5}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+........+\frac{1}{2^6}\right)\)

\(\Leftrightarrow A=1-\frac{1}{2^6}\)

Answer 3

\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\)

\(2A=1+\frac{1}{2}+\frac{1}{2^2}+................+\frac{1}{2^5}\)

\(2A-A=1-\frac{1}{2^6}\)

Answer 4

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}+\frac{1}{32}-\frac{ }{ }\)\(-\frac{1}{64}\)

\(A=1-\frac{1}{64}=\frac{63}{64}\)

Answer 5

\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)

\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)- \(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)

\(2A-A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}-\frac{1}{64}\)

=> \(A=1-\frac{1}{64}\)

     \(A=\frac{65}{64}-\frac{1}{64}=1\)

Answer 6

\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}+\frac{1}{32}-\frac{1}{64}+\frac{1}{64}\)

\(=1-\frac{1}{64}\)

\(=\frac{63}{64}\)

Answer 7

\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}+\frac{1}{32}-\frac{1}{64}\)

\(A=1-\frac{1}{64}\)

\(A=\frac{63}{64}\)

Answer 8

1/2+1/4+1/8+1/16+1/32+1/64

=32/64+16/64+4/64+2/64+1/64

=51/64

Answer 9

Nhầm cái cuối

\(1-\frac{1}{64}=\frac{64}{64}-\frac{1}{64}=\frac{63}{64}\)

Sorry bạn nha

Answer 10

A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64

2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32

2A - A = A = ( 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 ) - ( 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 )

A = 1 - 1/64

A = 63/64