(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

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

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

(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

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

= \(-\frac{3}{4}.-\frac{8}{9}...-\frac{120}{121}\)

= \(\frac{-3.8....120}{4.9...121}\)

= \(\frac{-1.3.2.4...10.12}{2^2.3^3...11^2}\)

= \(-\frac{12}{2.11}\)

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

Tính

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

\(\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right).\left(\frac{1}{16}-1\right).....\left(\frac{1}{121}-1\right)\\ =\frac{-3}{4}.\frac{-8}{9}.\frac{-15}{16}.....\frac{-120}{121}\)

\(=\frac{-1.3}{2.2}.\frac{-2.4}{3.3}.\frac{-3.5}{4.4}.....\frac{-10.12}{11.11}\)

\(=\frac{\left(-1.3\right).\left(-2.4\right).\left(-3.5\right).....\left(-10.12\right)}{2^2.3^2.4^2.....11^2}\\ =\frac{\left(-1\right).\left(-2\right).\left(-3\right).....\left(-10\right)}{2.3.4.....11}.\frac{3.4.5.....12}{2.3.4.....11}\)

\(=\frac{1}{2}.\frac{12}{11}\\ =\frac{6}{11}\)

\(\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right).\left(\frac{1}{16}-1\right)....\left(\frac{1}{121}-1\right)\)
\(=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{120}{121}\\= \frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}....\frac{10.12}{11^2}\\ =\frac{\left(1.3\right).\left(2.4\right).\left(3.5\right)....\left(10.12\right)}{2^2.3^2.4^2......11^2}\\ =\frac{1.2.3.....10}{2.3.4.....11}.\frac{3.4.5.....12}{2.3.4.....11}\\ =\frac{1}{11}.\frac{12}{2}\\ =\frac{1}{11}.6\\ =\frac{6}{11}\)
 

S=\(^{2^{2010}-2^{2009}-2^{2008}-...-2-1}\)

 = 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