Question

Tinh

1/2 +1/4+1/8+1/16+......+1/128

 

Answer 1

1/2+1/4+1/8+1/16+....+1/128

=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+...+1/64-1/128

=1-1/128

=127/128

Answer 2

Đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+.......+\frac{1}{128}\)

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

\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+.......+\frac{1}{64}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+.....+\frac{1}{128}\right)\)

\(A=1-\frac{1}{128}=\frac{127}{128}\)

Answer 3

\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+....+\frac{1}{128}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-......+\frac{1}{64}-\frac{1}{128}\)

\(=1-\frac{1}{128}\)

\(=\frac{127}{128}\)

Answer 4

                  Đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\)

                   \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^7}\)

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

             \(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^6}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^7}\right)\)

                \(A=1-\frac{1}{2^7}\)

            Ủng hộ mk nha !!!! ^_^

Answer 5

Đặt \(X=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{128}\)
\(X=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^7}\)
\(2X=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^6}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^6}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^7}\right)\)
\(X=1-\frac{1}{2^7}\)