Ta có:  1/1.2 = 1- 1/2 

           1/3.4 = 1/3 - 1/4 

          ...............

             1/19.20 = 1/19 - 1/20 

Cộng vế với vế ta đc: 

    A = 1- 1/20 = 19/20   

\(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{17.18}+\frac{1}{19.20}\)

\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{17}-\frac{1}{18}+\frac{1}{19}-\frac{1}{20}\)

\(A=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{17}+\frac{1}{19}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+..+\frac{1}{18}+\frac{1}{20}\right)\)

\(A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{18}+\frac{1}{20}\right)\)

\(A=\left(1+\frac{1}{2}+...+\frac{1}{20}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{9}+\frac{1}{10}\right)\)

\(A=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{19}+\frac{1}{20}\)

\(\frac{A}{B}=1\)

\(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{19.20}\)

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

\(\Rightarrow A=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{19}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{20}\right)\)

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

\(\Rightarrow A=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{20}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)\)

\(\Rightarrow A=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}=B\)

\(\Rightarrow\frac{A}{B}=1\)

mấy bài đó dễ mà ha!

Tính tử số:

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

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

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

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

\(=1+\frac{1}{2}+...+\frac{1}{20}-\left(1+\frac{1}{2}+...+\frac{1}{10}\right)\)

\(=\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}\)

\(\Rightarrow A=\frac{\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}}{\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}}=1\)

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

=1-1/20

=19/20

Xin lỗi máy tớ chỉ có cách viết phân số thế này / thông cảm

Ta có : A= 1/1 -1/2 + 1/2 -1/3 + 1/3 - 1/4 + 1/4 -1/5 +... + 1/19 - 1/20

=>       A= 1/1 - 1/20

=>        A = 19/20

Vậy A = 19/20

\(\frac{19}{20}\)nhé

 Đặt A = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + ... + 1/98.99.100 
Áp dụng phương pháp khử liên tiếp: viết mỗi số hạng thành hiệu của hai số sao cho số trừ ở nhóm trước bằng số bị trừ ở nhóm sau. 
Ta xét: 
1/1.2 - 1/2.3 = 2/1.2.3; 1/2.3 - 1/3.4 = 2/2.3.4;...; 1/98.99 - 1/99.100 = 2/98.99.100 
tổng quát: 1/n(n+1) - 1/(n+1)(n+2) = 2/n(n+1)(n+2). Do đó: 
2A = 2/1.2.3 + 2/2.3.4 + 2/3.4.5 +...+ 2/98.99.100 
= (1/1.2 - 1/2.3) + (1/2.3 - 1/3.4) +...+ (1/98.99 - 1/99.100) 
= 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + ... + 1/98.99 - 1/99.100 
= 1/1.2 - 1/99.100 
= 1/2 - 1/9900 
= 4950/9900 - 1/9900 
= 4949/9900. 
Vậy A = 4949 / 9900   

     Mk ko biết ghi phân số trên máy nên chỉ ghi được như thế này thôi nhưng mà mong bạn k cho mk nha

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

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

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

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

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

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

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

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

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

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

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

mk làm tắt dc ko

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}\)

\(=\frac{99}{100}\)