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\(A=\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}...\frac{9^2}{9.10}=\frac{1^2.2^2.3^2...9^2}{1.2.2.3.3.4.4...9.10}=\frac{1.2^2.3^2...9^2}{1.2^2.3^2.4^2...10^2}=\frac{1}{10^2}=\frac{1}{100}\)
A=\(\frac{1.2.3.4...8.9}{2.3.4.5...9.10}\)
A=\(\frac{1}{10}\)
mình làm đc 1 câu thôi. Bạn thông cảm nhé
\(B=\frac{2.2}{1.3}.\frac{3.3}{2.4}...\frac{2015.2015}{2014.2016}\)
\(B=\frac{2.3...2015}{1.2...2014}.\frac{2.3...2015}{3.4...2016}\)
\(B=2015.\frac{1}{1008}\)
\(B=\frac{2015}{1008}\)
G = \(\frac{2^2}{1.3}\).\(\frac{3^2}{2.4}\).\(\frac{4^2}{3.5}\).....\(\frac{50^2}{49.51}\)
=> G = \(\frac{2.2}{1.3}\).\(\frac{3.3}{2.4}\).\(\frac{4.4}{3.5}\).....\(\frac{50.50}{49.51}\)
=> G = \(\frac{2.2.3.3.4.4.....50.50}{1.2.3.3.4.4.....50.51}\)
=> G = \(\frac{2.50}{1.51}\)
=> G = \(\frac{100}{51}\)
\(\frac{2^2}{1.3}\times\frac{3^2}{2.4}\times............................\times\frac{50^2}{49.50}\)
\(=\frac{2.2}{1.3}\times\frac{3.3}{2.4}\times....................\times\frac{50.50}{49.50}\)
\(=\frac{\left(2.3.4..............50\right)\left(2.3.4............50\right)}{\left(1.2.3.............49\right)\left(3.4.5...........50\right)}\)
\(=\frac{50}{49}.2\)
\(=\frac{100}{49}\)
\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.....\frac{999^2}{999.1000}\)
\(=\frac{1.1}{1.2}.\frac{2.2}{2.3}.\frac{3.3}{3.4}.....\frac{999.999}{999.1000}\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{999}{1000}\)
\(=\frac{1}{1000}\)