Gọi biểu thức trên là A, ta có:

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

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

A x 2 - A = A x 1 = A = \(1-\frac{1}{16}=\frac{15}{16}\)

B = 5\(\dfrac{1}{2}\) + \(\dfrac{4}{5}\) - 2,5 + 1,2

B = 5,5 + 0,8 - 2,5 + 1,2

B = (5,5 - 2,5) + (0,8 + 1,2)

B = 3 + 1

B = 4

a)

Vì 2/9=6/27=8/36=12/54=16/72=18/81 nên:

2/9+6/27+8/36+12/54+16/72+18/81=

2/9+2/9+2/9+2/9+2/9+2/9=

2/9*6=

12/9=

4/3

Vậy 2/9+6/27+8/36+12/54+16/72+18/81=4/3

b)

Ta có:

1-2/5=3/5

1-2/7=5/7

1-2/9=7/9

...

1-2/99=97/99

Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=

3/5*5/7*7/9*...*97/99=

(3*5*7*...*97)/(5*7*9*...*99)=

3/99=

1/33

Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=1/33

c)

Gọi biểu thức 1/2+1/4+1/8+1/16+...+1/1024 là S,ta có:

S=1/2+1/4+1/8+1/16+...+1/1024

S*2=1+1/2+1/4+1/8+...+1/512

S*2-S=(1+1/2+1/4+1/8+...+1/512)-(1/2+1/4+1/8+1/16+...+1/1024)

S=1-1/1024

S=1023/1024

Vậy 1/2+1/4+1/8+1/16+...+1/1024=1023/1024

Cảm ơn bạn nhé!

s=1/2¹ + 1/2²+1/2³+.........+1/2¹⁰

2s=  1/2²   +1/2³+.........+1/2¹⁰+1/2¹¹

2s-s= ( 1/2²   +1/2³+.........+1/2¹⁰+1/2¹¹ ) -(1/2¹ + 1/2²+1/2³+.........+1/2¹⁰)

s= 1/2¹¹        -1/2

\(\frac{13}{90}\)+ \(\frac{1}{4}\)+ \(\frac{77}{90}\)

= \(\left(\frac{13}{90}+\frac{77}{90}\right)+\frac{1}{4}\)

= 1 + \(\frac{1}{4}\)

= \(\frac{5}{4}\)

a )  13/90 + 1/4 + 77/90                                       

= ( 13/90 + 77/90 ) + 1/4 

=   90/90 + 1/4 

= 1 + 1/4 

= 5/4 

b )        16/81 + 5/13 + 65/ 81 + 8/13 

       =  ( 16/81 + 65/81 ) + ( 5/13+8/13 ) 

       =           81/81         + 13/13 

       =             1 + 1 

       =  2 

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