[1-1/4]x[1-1/9]x[1-1/16]x.....x[1-1/100]x[1-1/121]
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\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{99}{100}\times\frac{120}{121}=\frac{3\times8\times15\times...\times99\times120}{4\times9\times16\times...\times100\times121}\)
\(\frac{\left(1\times3\right)\times\left(2\times4\right)\times\left(3\times5\right)\times...\times\left(9\times11\right)\times\left(10\times12\right)}{\left(2\times2\right)\times\left(3\times3\right)\times\left(4\times4\right)\times...\times\left(10\times10\right)\times\left(11\times11\right)}=\frac{\left(1\times2\times3\times...\times10\right)\times\left(3\times4\times5\times...\times12\right)}{\left(2\times3\times...\times11\right)\times\left(2\times3\times...\times11\right)}=\frac{12}{11\times2}=\frac{6}{11}\)
(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
Bạn ấn vào chữ "Câu hỏi tương tự" để tham khảo nhé
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\(\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{100}\right)\left(1-\frac{1}{121}\right)\)
=\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{99}{100}.\frac{120}{121}\)
=\(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{3.3}.....\frac{9.11}{10.10}.\frac{10.12}{11.11}\)
=\(\frac{\left(1.2.3.....9.10\right)\left(3.4.5.....11.12\right)}{\left(2.3.4.5.....10.11\right)\left(2.3.4.5....10.11\right)}\)
=\(\frac{12}{11.2}\)
=\(\frac{6}{11}\)
\(\left(1-\frac{1}{6}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).....\left(1-\frac{1}{100}\right).\left(1-\frac{1}{121}\right)\)
\(=\frac{5}{6}.\frac{8}{9}.\frac{15}{16}.....\frac{99}{100}.\frac{120}{121}\)
\(=\frac{5}{6}.\left(\frac{2.4}{3^3}.\frac{3.5}{4^2}.....\frac{9.11}{10^2}.\frac{10.12}{11^2}\right)\)
\(=\frac{5}{6}.\left[\left(\frac{2}{3}.\frac{3}{4}.....\frac{9}{10}.\frac{10}{11}\right).\left(\frac{4}{3}.\frac{5}{4}....\frac{11}{10}.\frac{12}{11}\right)\right]\)
\(=\frac{5}{6}.\frac{2}{11}.\frac{12}{3}\)
\(=\frac{5}{33}.4\)
\(=\frac{20}{33}\)
à nhầm cái này bạn chỉ cần viết ra rồi giản ước là xong :)
(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
\(\dfrac{ }{_{ }\sinh}\lim\limits_{\rightarrow\max\limits_{ }\tanh}\)