sao?

\(\frac{1}{2}\)* \(\frac{1}{4}\)* \(\frac{1}{8}\)* \(\frac{1}{16}\)* \(\frac{1}{32}\)= \(\frac{1}{32768}\)

                                          k cho mình nhé !

bằng 1/32768

a=511/256

b=647/20

c=mình đang suy nghĩ,nhưng nếu bạn k cho mình thì bạn sẽ có câu trả lời

a. 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256

= 1 + ( 1 - 1/2) + ( 1/2 - 1/4) + ( 1/4 - 1/8) + ( 1/8 - 1/16) + ( 1/16 - 1/32) + (1/32 - 1/64) + ( 1/64 - 1/128) + (1/128 - 1/256)

= 1 + 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 - 1/32 + 1/32 - 1/64 + 1/64 - 1/128 + 1/128 - 1/256

= 2 - 1/256

= 511/256

Câu b bạn có viết sai đề không vậy?

Câu a:

A = \(\frac{1}{2\times3}\) + \(\frac{1}{3\times4}\) + \(\frac{1}{4\times5}\) + \(\frac{1}{5\times6}\) + \(\frac{1}{6\times7}\) + \(\frac{1}{7\times8}\)

A = \(\frac12-\frac13\) + \(\frac13-\frac14\) + \(\frac14-\frac15\) + \(\frac15-\frac16\) + \(\frac16-\frac17\) + \(\frac17-\frac18\)

A = \(\frac12-\frac18\)

A = \(\frac38\)

Câu b:

A = \(\frac12\) + \(\frac14\) + \(\frac18\) + \(\frac{1}{16}\) + \(\frac{1}{32}\) + \(\frac{1}{64}\) + \(\frac{1}{128}\) + \(\frac{1}{256}\)

2 x A = 1 + \(\frac12\) + \(\frac14\) + \(\frac18\) + \(\frac{1}{16}\) + \(\frac{1}{32}\) + \(\frac{1}{64}\) + \(\frac{1}{128}\)

2 x A - A = 1 + \(\frac12\) +\(\frac14\) + \(\frac18\) + \(\frac{1}{16}\) + \(\frac{1}{32}\) + \(\frac{1}{64}\) + \(\frac{1}{128}\) - \(\frac12-\frac14\) -...-\(\frac{1}{128}\) -\(\frac{1}{256}\)

A x (2 - 1) = (1 - \(\frac{1}{256}\)) + (\(\frac12\)-\(\frac12\)) +...+(\(\frac{1}{128}\) - \(\frac{1}{128}\))

A = 1 - \(\frac{1}{256}\) + 0 + 0+...+ 0

A = \(\frac{255}{256}\)

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

2A-A=(1+1/2+1/4+1/8+1/16+1/32+1/64)-(1/2+1/4+1/8+1/16+1/32+1/64+1/128)

A=1-1/128

A=127/128

A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128

suy ra: 2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64

2A - A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 - 1/2 - 1/4 - 1/8 - 1/16 - 1/32 - 1/64 - 1/128

A = 1 - 1/128 = 127/128

hok tốt

\(\frac{255}{256}\)

bạn lấy mọi phân số quy đồng lên lấy mẫu là 256

      A  =          \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) +    \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\)+.....+  \(\dfrac{1}{134}\)+ \(\dfrac{1}{268}\)

A \(\times\) 2 =  1  +  \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\)   + \(\dfrac{1}{8}\)  + \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\) +.....+ \(\dfrac{1}{134}\)

A \(\times\) 2 - A = 1 - \(\dfrac{1}{268}\)

A \(\times\) ( 2  - 1) = \(\dfrac{267}{268}\)

A = \(\dfrac{267}{268}\)

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

Ta thấy:

1/2=1/1-1/2

1/4=1/2-1/4

1/8=1/4-1/8....

1/64=1/32-1/64

A= 1/1-1/2+1/2-1/4+1/4-1/8+.....+1/32-1/64

A=1 - 1/ 64

A= 63/64

\(\frac{32}{64}+\frac{16}{64}+\frac{8}{64}+\frac{4}{64}+\frac{2}{64}+\frac{1}{64}=\frac{63}{64}\)\(\frac{63}{64}\)