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22 tháng 4 2023

(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

11 tháng 8

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

26 tháng 4 2015

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

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

(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

25 tháng 7 2020

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+]++++++++++ )

13 tháng 7 2015

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

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

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

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

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

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

1 tháng 11 2022

Cho em Hải 1100x1phần9 là bao nhiêu

29 tháng 7 2020

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

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

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

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

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

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

29 tháng 7 2020

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 

3 tháng 3 2016

a)  ta thấy 1/2x3 + 1/3x4 + 1/4 x 5 + ...... + 1/a x ( a + 1 ) = 1/2 - 1/3 + 1/3 -1/4 +............+ 1/a - 1/a+1 = 49/100

1/2 - 1/a+1= 49/100

1/a+1=1/2 - 49/100

1/a + 1= 1/100

a + 1= 100

a= 100 - 1

a= 99

b) ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1 - 1/16) x ..... x (1 - 1/625) 

= 3/4 x 8/9 x 15/16 x...........x 575/576x 624/625 = 1x3/1x4 x 2x4/ 3x3 x 3x5/4 x 4x.................x 23x 25/ 24 x 24 x  24x26/ 25x25

= ( 1/1 x 2/3 x 3/4 x 4/5 x .................x 23/24 x 24/25= 1x2x3x4x..............23x24/ 1 x 3 x 4 x5x............24x25=2/25)

( 3/5 x 4/3 x 5/4 x 6/5x.............x 25/24 x 26/25= 3 x 4 x 5x 6 x ............x 25x 26/ 5 x 3 x 4 x 5x............x 24 x 25= 26/5)

2/25 x 26/5= 52/30= 26/25

19 tháng 3 2017

câu B bằng 13/25 hoặc 0,52