Question

 \(B=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)

Answer 1

a) Đặt A= 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 
2A= 2(1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256) 
     = 1+1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 
=>A =  2A-A =1+1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 -1/2 - 1/4 - 1/8 - 1/16 - 1/32 - 1/64 - 1/128 - 1/256 
=1-1/256 
=255/256

Answer 2

63/64

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

\(B+\frac{1}{128}=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{128}.\)

\(B+\frac{1}{128}=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{64}\)

\(B+\frac{1}{128}=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{32}\)

...

\(B+\frac{1}{128}=1\)

Vậy, \(B=1-\frac{1}{128}=\frac{127}{128}\)

Answer 7

Ta co:

   1/2=1-/2

   1/4=1/2-1/4

   1/8=1/4-1/8.....

Vậy tổng trên=1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64+1/64-1/128

                 =1/2-1/128

                =63/128