a) Đặt A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32

A = 1/2 + 1/2² + 1/2³ + 1/2⁴ + 1/2⁵

2A = 2(1/2 + 2² + 1/2³ + 1/2⁴ + 1/2⁵)

2A = 1 + 1/2 + 1/2² + 1/2³ + 1/2⁴

2A - A = (1 + 1/2 + 1/2²  + 1/2³ + 1/2⁴) - (1/2  + 1/2²  + 1/2³ + 1/2⁴ + 1/2⁵)

A = 1 - 1/2⁵

A = 31/32

b) 2/1.2 + 2/2.3 + 2/3.4 + ... + 2/18 . 19 + 2/19.20

= 2(1/1.2  + 1/2.3  + 1/3.4 + ... + 1/18.19 + 1/19.20)

= 2.(1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/18 - 1/19 + 1/19 - 1/20)

= 2. (1 - 1/20)

= 2.19/20

= 19/10

bạn thiếu ý C 

Sửa đề câu c) 

2 - 4 + 6 - 8 + 10 - 12 + ...... + 98 - 100 + 102 

= 2 + ( 6 - 4 ) + ( 10 - 8 ) + ..... + ( 98 - 96 ) + ( 102 - 100 )

= 2 + ( 2 + 2 + 2 + 2 + .... + 2 )

= 2 + 50

= 52

1.a)x.x=4/9

Ta có:2/3.2/3=4/9

Vậy x= 4/9

b)x.7,99=7,99

x=7,99:7,99

x=1

2.a)đặt tên biểu thức là A.

A=1/2.1/4.1/8.1/16.1/32

2.A=1+1/2+1/4+1/8+1/16

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

A=1-1/32=31/32.

b)đặt tên biểu thức là S.

S=2/1.2+2/2.3+2/3.4+...+2/18.19+2/19.20

S=2.(1/1.2+1/2.3+1/3.4+...+1/18.19+1/19.20)

S=2.(1/1-1/2+1/2-1/3+1/3-1/4+...+1/18-1/19+1/19-1/20)

S=2.(1/1-1/20)

S=2.19/20

S=19/10.

Chúc bạn học giỏi nha!!!

k cho mình nha!!!

Đặt \(A=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{18.19}+\frac{2}{19.20}\)

\(\Rightarrow A=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

\(\Rightarrow A=2.\left(1-\frac{1}{20}\right)\)

\(\Rightarrow A=2.\frac{19}{20}\)

\(\Rightarrow A=\frac{19}{10}\)

2.(1/1.2+1/2.3+.....+1/18.19+1/19.20)

2.(1/1-1/2+1/2-1/3+......+1/19-1/20)

2.(1/1-1/20)= 2.19/20=19/10

Mỏi tay nhắm . không viết đầu bài đâu >.<

= \(2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}+\frac{1}{19.20}\right)\)

= \(2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

= \(2\left(1-\frac{1}{20}\right)\)

= \(2.\frac{19}{20}\)

= \(\frac{19}{10}\)

Mị không chắc đâu :3

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}+\frac{1}{19.20}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\)

\(A=1-\frac{1}{20}\)

\(A=\frac{19}{20}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{19}-\frac{1}{20}\)

\(=1-\frac{1}{20}\)

\(=\frac{19}{20}\)

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}+\frac{1}{19.20}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\)

\(A=1-\frac{1}{20}\)

\(A=\frac{19}{20}\)

dạng tổng quát của mỗi phân số là 1/n(n+1) = 1/n -1/n+1

áp dụng vào làm với các phân số trong biểu thức cuối cùng còn 1-1/10=19/20

Đặt  \(A=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{18.19}+\frac{2}{19.20}\)

\(A=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}+\frac{1}{19.20}\right)\)

\(A=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}\right)\)

\(A=2\left(1-\frac{1}{20}\right)\)

\(A=2.\frac{19}{20}=\frac{19}{10}\)

Vậy ...

=2.(\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+......+\(\frac{1}{19.20}\))

=2.( 1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+..........+\(\frac{1}{19}\)-\(\frac{1}{20}\))

=2.(1-\(\frac{1}{20}\))

=2.\(\frac{19}{20}\)

=  \(\frac{19}{10}\)

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{18.19}+\frac{2}{19.20}\)

\(=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

\(=2.\left(1-\frac{1}{20}\right)\)

\(=2\cdot\frac{19}{20}=\frac{19}{10}\)

Ta có:A: 1/1.2 +1/2.3 +1/3.4+...+1/18.19+1/19.20
     => A= 1-1/2 +1/2-1/3+1/3-1/4+...+1/18-1/19+1/19-1/20

     =>A= 1-1/20=19/20

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+..+\frac{1}{19.20}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}\)

\(=1-\frac{1}{20}=\frac{19}{20}\)

=1-1/2+1/2-1/3+1/3-1/4+.........+1/18-1/19+1/19-1/20

=1-1/20

=19/20