(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

Mk trả lời giống như trên! Câu trả lời quá chuẩn

 Ta thấy :

4 - 1 = 3

9 - 4 = 5

16 - 9 = 7

...

Các số tiếp theo là 25 ; 36 ; 49 ; 64 ; 81 ; 100 

Tổng trên :

1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 + 121 = 506

(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

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

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

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

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

(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

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

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