(1-1/4).(1-1/9).(1-1/16)....(1-1/100).(1-1/121)

=3/4.8/9.15/16...99/100.120/121

=(1.3/2.2).(2.4/3.3).(3.5/4.4)....(9.11/10.10).(10.12/11.11)

=1.3.2.4.3.5...9.11.10.12/2.2.3.3.4.4...10.10.11.11

=(2.3.4...9.10.11).(3.4.5...10.12)/(2.3.4...9.10.11).(2.3.4....10.11)

=12/2.11

=6/11

nha

\(\dfrac{ }{_{ }\sinh}\lim\limits_{\rightarrow\max\limits_{ }\tanh}\)

\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{99}{100}\times\frac{120}{121}=\frac{3\times8\times15\times...\times99\times120}{4\times9\times16\times...\times100\times121}\)

\(\frac{\left(1\times3\right)\times\left(2\times4\right)\times\left(3\times5\right)\times...\times\left(9\times11\right)\times\left(10\times12\right)}{\left(2\times2\right)\times\left(3\times3\right)\times\left(4\times4\right)\times...\times\left(10\times10\right)\times\left(11\times11\right)}=\frac{\left(1\times2\times3\times...\times10\right)\times\left(3\times4\times5\times...\times12\right)}{\left(2\times3\times...\times11\right)\times\left(2\times3\times...\times11\right)}=\frac{12}{11\times2}=\frac{6}{11}\)

(1-1/4).(1-1/9).(1-1/16)....(1-1/100).(1-1/121)

=3/4.8/9.15/16...99/100.120/121

=(1.3/2.2).(2.4/3.3).(3.5/4.4)....(9.11/10.10).(10.12/11.11)

=1.3.2.4.3.5...9.11.10.12/2.2.3.3.4.4...10.10.11.11

=(2.3.4...9.10.11).(3.4.5...10.12)/(2.3.4...9.10.11).(2.3.4....10.11)

=12/2.11

=6/11

\(\frac{6}{11}\)

Bạn ấn vào chữ "Câu hỏi tương tự" để tham khảo nhé

( nếu ko bt thì copy link này : https://olm.vn/hoi-dap/tim-kiem?id=259990292185&id_subject=1&q=+++++++++++[+1-1/4+]+x+[1-1/9+]x+[+1-+1/16+]+x..........x+[+1-1/100+]+x+[+1-+1/121+]++++++++++ )

\(\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{100}\right)\left(1-\frac{1}{121}\right)\)

=\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{99}{100}.\frac{120}{121}\)

=\(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{3.3}.....\frac{9.11}{10.10}.\frac{10.12}{11.11}\)

=\(\frac{\left(1.2.3.....9.10\right)\left(3.4.5.....11.12\right)}{\left(2.3.4.5.....10.11\right)\left(2.3.4.5....10.11\right)}\)

=\(\frac{12}{11.2}\)

=\(\frac{6}{11}\)

Cho em Hải 1100x1phần9 là bao nhiêu

\(B=\frac{10}{18}\times\frac{22}{30}\times\frac{36}{44}\times...\times\frac{200}{209}=\frac{1\times10}{2\times9}\times\frac{2\times11}{3\times10}\times\frac{3\times12}{4\times11}\times...\times\frac{10\times20}{11\times19}\)

\(=\frac{1\times10\times2\times11\times3\times12\times...\times10\times20}{2\times9\times3\times10\times4\times11\times...\times11\times19}=\frac{\left(1\times2\times3\times...\times10\right)\times\left(10\times11\times12\times...\times20\right)}{\left(2\times3\times4\times...\times11\right)\times\left(9\times10\times11\times...\times19\right)}\)

\(=\frac{1\times20}{11\times9}=\frac{20}{99}\)

Sửa đề \(C=\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times...\times\left(1-\frac{1}{100}\right)\)

\(=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{99}{100}=\frac{3\times8\times15\times...\times99}{4\times9\times16\times...\times100}=\frac{1\times3\times2\times4\times3\times5\times...\times9\times11}{2\times2\times3\times3\times4\times4\times...\times10\times10}\)

\(=\frac{\left(1\times2\times3\times....\times9\right)\times\left(3\times4\times5\times...\times11\right)}{\left(2\times3\times4\times...\times10\right)\times\left(2\times3\times4\times...\times10\right)}=\frac{1\times11}{10\times2}=\frac{11}{20}\)

b) C=(1- 1/4) x (1- 1/9) x (1-1/16) x (1- 1/100)

C = 3/4 . 8/9 . 15/16.......99/100

C= 3.8.15....99/4.9.16...100

C= 1.3.2.4.3.5....9.11/ 2.2.3.3.4.4......10.10

C= 1.2.3.4...9/ 2.3.4.5....10 . 3.4.5....11/ 2.3.4.5...10

C= 1/10 . 11/2

C= 11/20

Mk nghĩ đề nt mới đúng 

Câu a) để sau

b)\(C=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)\left(1-\frac{1}{100}\right)\)

\(C=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\frac{99}{100}\)

\(C=\frac{3\cdot8\cdot15\cdot99}{4\cdot9\cdot16\cdot100}\)

\(C=\frac{3\cdot4\cdot2\cdot3\cdot5\cdot11\cdot9}{2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot5\cdot20}=\frac{11\cdot9}{2\cdot4\cdot20}=\frac{99}{160}\)