giải mình bài này xong mình k cho

Ta có 5/2 + 5/4 + 5/8 + 5/16 + 5/32 + 5/64 + 5/128 + 5/256

= 5- 5/2  + 5/2 - 5/4  + 5/4 - 5/8 + 5/8 - 5/16 + 5/16 - 5/32  + 5/32 - 5/64 + 5/64 - 5/128 + 5/128 - 5/256

= 5-5/256

= 1275/256

b ) Đặt \(A=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{101.103}\)

\(\Rightarrow A=\frac{5}{2}\left(\frac{5}{1}-\frac{5}{3}+\frac{5}{3}-\frac{5}{5}+....+\frac{5}{101}-\frac{5}{103}\right)\)

\(\Rightarrow A=\frac{5}{2}\left(5-\frac{5}{103}\right)\)

= 5 x ( 2+4+6+8 )

= 5 x 20 = 100

\(2.5+4.5+6.5+8.5\)

\(=\left(2+4+6+8\right).5\)

\(=20.5=100\)

Em xin tham khảo:

5 x ( 2 + 4 + 6 + 8 )

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

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

=> 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)

=> A = 1 - 1/256

=> A = 255/256

Vậy: ...

\(\left(\dfrac{2}{7}+\dfrac{5}{7}\right)+\left(\dfrac{3}{5}+\dfrac{2}{5}\right)+\left(\dfrac{3}{8}+\dfrac{4}{8}+\dfrac{1}{8}\right)+\left(\dfrac{1}{9}+\dfrac{8}{9}\right)=1+1+1+1=4\)

(2/7 + 5/7) + (3/5 + 2/5) + (3/8 + 4/8 + 1/8) + (1/9 + 8/9 )

= 1  +       1                   +         1             +        1         =  4

(3/5+2/5)+(3/4+1/2)+5/8

=1+1+5/8

=2,6

= (3/5 + 2/5) + (3/4 + 1/2)

=         1         +       5/4

=                   9/4

ko biết có cần đổi ra số thập phân hay ko?

3/5+3/4+2/5+5/8+1/2

= 3/5+2/5 - 5/8+1/2+3/4

= 1 - 5/8 + 4/8+6/8

= 8/8-5/8+4/8+6/8

= 3/8+4/8+6/8

= 7/8+6/8

=13/8