\(\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)....\left(\frac{1}{121}-1\right)\)
= \(-\frac{3}{4}.-\frac{8}{9}...-\frac{120}{121}\)
= \(\frac{-3.8....120}{4.9...121}\)
= \(\frac{-1.3.2.4...10.12}{2^2.3^3...11^2}\)
= \(-\frac{12}{2.11}\)
= \(-\frac{6}{11}\)
Tính
(1/4-1).(1/9-1).(1/16-1).....(1/121-1)
\(\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right).\left(\frac{1}{16}-1\right).....\left(\frac{1}{121}-1\right)\\ =\frac{-3}{4}.\frac{-8}{9}.\frac{-15}{16}.....\frac{-120}{121}\)
\(=\frac{-1.3}{2.2}.\frac{-2.4}{3.3}.\frac{-3.5}{4.4}.....\frac{-10.12}{11.11}\)
\(=\frac{\left(-1.3\right).\left(-2.4\right).\left(-3.5\right).....\left(-10.12\right)}{2^2.3^2.4^2.....11^2}\\ =\frac{\left(-1\right).\left(-2\right).\left(-3\right).....\left(-10\right)}{2.3.4.....11}.\frac{3.4.5.....12}{2.3.4.....11}\)
\(=\frac{1}{2}.\frac{12}{11}\\ =\frac{6}{11}\)
\(\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right).\left(\frac{1}{16}-1\right)....\left(\frac{1}{121}-1\right)\)
\(=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{120}{121}\\=
\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}....\frac{10.12}{11^2}\\
=\frac{\left(1.3\right).\left(2.4\right).\left(3.5\right)....\left(10.12\right)}{2^2.3^2.4^2......11^2}\\
=\frac{1.2.3.....10}{2.3.4.....11}.\frac{3.4.5.....12}{2.3.4.....11}\\
=\frac{1}{11}.\frac{12}{2}\\
=\frac{1}{11}.6\\
=\frac{6}{11}\)
