ĐẶT BIỂU THỨC TRÊN LÀ M
TA CÓ \(2M=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+.....+\frac{1}{64}\)
\(\Rightarrow2M-M=1+\frac{1}{2}+\frac{1}{4}+..+\frac{1}{64}-\frac{1}{2}+\frac{1}{4}+..+\frac{1}{128}\)
\(\Rightarrow M=1+\frac{1}{28}\)
A= \(\frac{1}{2}\)+\(\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\)
2A=2(\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\))
=1+\(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{64}\)
2A-A= (\(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{64}\)) -(\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\))
A=1-\(\frac{1}{128}\)
A=\(\frac{127}{128}\)
A=1/2+1/4+1/8+.......+1/128
2A=2*(1/2+1/4+1/8+.........+1/128)
2A=1+1/2+1/4+..........+1/64
2A-A=(1+1/2+1/4+...........+1/64)-(1/2+1/4+1/8+.............+1/128)
Bây giờ loại các phân số giống nhau ở hai bên
A=1-1/128
A=127/128
ta đặt A = 1/2 + 1/4 + 1/8 + ..... + 1/128
suy ra A x 2 = ( 1/2 + 1/4 + 1/8 + ..... + 1/128 ) x 2
A x 2 = ( 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + ...... + 1/64 - 1/128 ) x 2
A x 2 = ( 1 - 1/128 ) x 2
A x 2 = 127/128 x 2
A x 2 : 2 = 127/128 x 2 : 2
A = 127/128
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\)
\(2A=2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\right)\)
\(=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\)
\(2A-A=1-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\right)\)
\(=1-\frac{1}{128}=\frac{128}{128}-\frac{1}{128}=\frac{127}{128}\)
