( 1 - 1/4 ) x ( 1- 1/9 ) x ( 1 - 1/16 ) x ....... x ( 1-1/100 )
[1-1/4]x[1-1/9]x[1-1/16]x.....x[1-1/100]x[1-1/121]
(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
\(\dfrac{ }{_{ }\sinh}\lim\limits_{\rightarrow\max\limits_{ }\tanh}\)
( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1 - 1/16 ) x ...... x ( 1 - 1/100 )
( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1- 1/16 ) x ............ x (1 - 1/100 ) x ( 1 - 1/121 ) = ?
\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{99}{100}\times\frac{120}{121}=\frac{3\times8\times15\times...\times99\times120}{4\times9\times16\times...\times100\times121}\)
\(\frac{\left(1\times3\right)\times\left(2\times4\right)\times\left(3\times5\right)\times...\times\left(9\times11\right)\times\left(10\times12\right)}{\left(2\times2\right)\times\left(3\times3\right)\times\left(4\times4\right)\times...\times\left(10\times10\right)\times\left(11\times11\right)}=\frac{\left(1\times2\times3\times...\times10\right)\times\left(3\times4\times5\times...\times12\right)}{\left(2\times3\times...\times11\right)\times\left(2\times3\times...\times11\right)}=\frac{12}{11\times2}=\frac{6}{11}\)
(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
[ 1-1/4 ] x [1-1/9 ]x [ 1- 1/16 ] x..........x [ 1-1/100 ] x [ 1- 1/121 ]
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+]++++++++++ )
( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1 - 1/16 ) x ... x (1 - 1/100) x (1- 1/121) = ?
\(\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{100}\right)\left(1-\frac{1}{121}\right)\)
=\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{99}{100}.\frac{120}{121}\)
=\(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{3.3}.....\frac{9.11}{10.10}.\frac{10.12}{11.11}\)
=\(\frac{\left(1.2.3.....9.10\right)\left(3.4.5.....11.12\right)}{\left(2.3.4.5.....10.11\right)\left(2.3.4.5....10.11\right)}\)
=\(\frac{12}{11.2}\)
=\(\frac{6}{11}\)
F = (1-1/4) x (1-1/9) x (1-1/16) x ......... x ( 1-1/100) = ?
So sánh B = (1/4 -1) x (1/9 -1) x ( 1/16 -1) x ... x (1/81 -1) x (1/100 -1) với -11/21
Tính nhanh
a) B= 10/18 x 22/30 x 36/44 x ... x 200/209
b) C=(1- 1/4) x (1- 1/9) x (1-1/16) x (1- 1/100)
\(B=\frac{10}{18}\times\frac{22}{30}\times\frac{36}{44}\times...\times\frac{200}{209}=\frac{1\times10}{2\times9}\times\frac{2\times11}{3\times10}\times\frac{3\times12}{4\times11}\times...\times\frac{10\times20}{11\times19}\)
\(=\frac{1\times10\times2\times11\times3\times12\times...\times10\times20}{2\times9\times3\times10\times4\times11\times...\times11\times19}=\frac{\left(1\times2\times3\times...\times10\right)\times\left(10\times11\times12\times...\times20\right)}{\left(2\times3\times4\times...\times11\right)\times\left(9\times10\times11\times...\times19\right)}\)
\(=\frac{1\times20}{11\times9}=\frac{20}{99}\)
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)\(C=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)\left(1-\frac{1}{100}\right)\)
\(C=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\frac{99}{100}\)
\(C=\frac{3\cdot8\cdot15\cdot99}{4\cdot9\cdot16\cdot100}\)
\(C=\frac{3\cdot4\cdot2\cdot3\cdot5\cdot11\cdot9}{2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot5\cdot20}=\frac{11\cdot9}{2\cdot4\cdot20}=\frac{99}{160}\)
tính: A=1/4+1/12+1/24+....+1/220
B=(1-1/4)x(1-1/9)x(1-1/16)x...x(1-1/100)
C=(1-2/2.3)x(1-2/3.4)x(1-2/4.5)x....x(1-2/99.100)
cả . ,x đều là nhân