Đặt \(A=\left(1+\frac{7}{9}\right)\left(1+\frac{7}{20}\right)\left(1+\frac{7}{33}\right)\left(1+\frac{7}{48}\right)+...+\left(1+\frac{7}{2009}\right)\)

\(\Leftrightarrow1+\left(\frac{7}{9}.\frac{7}{20}.\frac{7}{33}.\frac{7}{48}.....\frac{7}{2009}\right)\)

Dãy phân số trên có số phân số là:

(2009 - 9) : 4 + 2 =502

\(\Rightarrow A=1+\left(\frac{7^{502}}{9.20.33.48.....2009}\right)\)

giúp mình với

A=16/9 .27/20 . 40/33 . 55/48 ....2016/2009

   =(16.27.40.55...2016)  /  (9.20.33.48...2009)

   = [(2.8)(3.9)(4.10)(5.11)...(42.48)]   /  [(1.9)(2.10)(3.11)(4.12)...(41.49)]

   =[(2.3.4.5..42)(8.9.10.11..48)]   /   [(1.2.3.4...41)(9.10.11.12...49)]

   =(42.8) / (1.49)

   =336/49

  =48/7

Cậu thông cảm,mk trình bày hơi khó nhìn

a) =\(\frac{1}{2}.\frac{2}{3}.....\frac{2017}{2018}=\frac{1.2.....2017}{2.3.4.....2018}=\frac{1}{2018}\)

a) \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2018}\right)\)

\(=\frac{1}{2}.\frac{2}{3}...\frac{2017}{2018}\)

\(=\frac{1.2...2017}{2.3...2018}\)

\(=\frac{1}{2018}\)

b) \(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{190}\right)\)

\(=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{189}{190}\)

\(=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}.\frac{28}{30}...\frac{378}{380}\)

\(=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}.\frac{7.4}{5.6}...\frac{18.21}{19.20}\)

\(=\frac{\left(1.2.3...18\right).\left(4.5.6...21\right)}{\left(2.3.4...19\right).\left(3.4.5...20\right)}\)

\(=\frac{1.21}{19.3}\)

\(=\frac{21}{57}\)

c) \(\left(1+\frac{7}{9}\right)\left(1+\frac{7}{20}\right)\left(1+\frac{7}{33}\right)\left(1+\frac{7}{48}\right)...\left(1+\frac{7}{2009}\right)\)

\(=\frac{16}{9}.\frac{27}{20}.\frac{40}{33}.\frac{56}{48}...\frac{2016}{2009}\)

mk ko bít làm câu c ! xin lỗi bn nha! bn tự nghĩ cách làm câu c giúp mk nhé!

Cô giải như sau Minh nhé :)

\(A=\left(1+\frac{7}{9}\right)\left(1+\frac{7}{20}\right)\left(1+\frac{7}{33}\right)...\left(1+\frac{7}{2900}\right)=\frac{16}{9}.\frac{27}{20}.\frac{40}{33}...\frac{2907}{2900}\)

\(=\frac{8.2}{9.1}.\frac{9.3}{10.2}.\frac{10.4}{11.3}....\frac{57.51}{58.50}=\frac{\left(8.9.10....57\right)\left(2.3.4...51\right)}{\left(9.10.11...58\right)\left(2.3.4....50\right)}=\frac{8.51}{58}=\frac{204}{29}\)

( 1 + 7/9 ) x ( 1 + 7/20 ) x ( 1 + 7/33 ) x...x ( 1 + 7/2900)

= (8x2)/(9x1) x (9x3)/(10x2) x (10x4)/(11x3) x...x (57x51)(58x50)

=(8x2x9x3x10x4x...x57x51) / (9x1x10x2x11x3x...x58x50) Sau khi giản ước ta được :

= (8x51) / (1x58) = 204/29