6/7 mình làm rồi 

trên violympic

5/14 đúng chắc luôn

1/2+1/6+1/12+1/20+1/30+1/42

Phan so thu 20 cua day la 1/1599

( olm duyệt nhanh gium em !!!!!!!!!)

1/3;1/15;1/35;1/63;......=1/1.3;1/3.5;1/5.7;1/7.9;..........

Phan so thu 20 cua day la 1/39.41=1/1599

chuẩn đó bạn 1/1599

20% = 1/5

28% = 7/25

\(\frac{1}{1.3};\frac{1}{3.5};\frac{1}{5.7};\frac{1}{7.9};...\)

=> Số thứ 20 là: \(\frac{1}{39.41}=\frac{1}{1599}\).

ket qua = \(\frac{1}{1599}\) ban nha

\(\frac{16}{45}\)

\(\frac{16}{45}\)

\(\Rightarrow x=\frac{16}{45}\)

\(\frac{16}{45}\)

Nhận xét : \(\frac{1}{6}=\frac{1}{2\cdot3}\);\(\frac{1}{12}=\frac{1}{3\cdot4}\);\(\frac{1}{20}=\frac{1}{4\cdot5};...\)

5 phân số còn lại : \(\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+\frac{1}{11\cdot12}\)

Tổng là :

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+...+\frac{1}{11\cdot12}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{12}\)

\(=\frac{1}{2}-\frac{1}{12}\)

\(=\frac{5}{12}\)

ta có:

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...\)

Từ đây ta có thể suy luận ra 5 p/số sau

Có: \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{132}\)

\(=\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+...+\frac{1}{11x12}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{12}\)

\(=\frac{1}{2}-\frac{1}{12}=\frac{12-2}{24}=\frac{10}{24}=\frac{5}{12}\)