(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+]++++++++++ )

      \(\left(1-\frac{1}{6}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).....\left(1-\frac{1}{100}\right).\left(1-\frac{1}{121}\right)\)

\(=\frac{5}{6}.\frac{8}{9}.\frac{15}{16}.....\frac{99}{100}.\frac{120}{121}\)

\(=\frac{5}{6}.\left(\frac{2.4}{3^3}.\frac{3.5}{4^2}.....\frac{9.11}{10^2}.\frac{10.12}{11^2}\right)\)

\(=\frac{5}{6}.\left[\left(\frac{2}{3}.\frac{3}{4}.....\frac{9}{10}.\frac{10}{11}\right).\left(\frac{4}{3}.\frac{5}{4}....\frac{11}{10}.\frac{12}{11}\right)\right]\)

\(=\frac{5}{6}.\frac{2}{11}.\frac{12}{3}\)

\(=\frac{5}{33}.4\)

\(=\frac{20}{33}\)

Thanks!

 = 1 - 1/121                                                                                                                                                                                                           =     120/121

Các bạn trình bày rõ ràng cho mình nha!

A= 3/4 x 8/9 x 15/16 x...x99/100 x 120/121

A=3x8x15x...x99x121/4x9x16x...x100x121

A= 1 x 3 x 2 x 4 x 3 x 5 x ... x 9 x 11 x 10 x 12/ 2 x 2 x 3 x 3 x 4 x 4 x ... x 10 x 10 x 11 x 11

A= (1x2x3x...x9x10)x(3x4x5x...x11x12)/(2x3x4x...x10x11)x(2x3x4x...x10x11)

A=1x12/11x2

A=6/11

Vậy A=6/11

giúp mik với ạ

ta có :

A=$\left(-\frac{3}{4}\right)\left(-\frac{8}{9}\right)\left(-\frac{15}{16}\right)...\left(-\frac{120}{121}\right)$(có 10 số hạng)

  = $\frac{3\cdot 8\cdot 15\cdot ...\cdot 120}{4\cdot 9\cdot 16\cdot ...\cdot 121}=\frac{\left(1.3\right)\left(2\cdot 4\right)\left(3\cdot 5\right)\cdot ...\cdot \left(10\cdot 12\right)}{{}^{}\cdot {}^{}\cdot {}^{}\cdot ...\cdot {}^{}}=\frac{\left(1\cdot 2\cdot 3\cdot ...\cdot 10\right)\left(3\cdot 4\cdot 5\cdot ...\cdot 12\right)}{\left(2\cdot 3\cdot 4\cdot ..\cdot 11\right)\left(2\cdot 3\cdot 4\cdot ..\cdot 11\right)}$

=$\frac{12}{11\cdot 2}=\frac{12}{22}$

= 1222

các bạn làm ơn giúp mình nhé

à nhầm cái này bạn chỉ cần viết ra rồi giản ước là xong :)