1<1/3+1/8+1/15+1/24+....+1/360>
KO BIẾT ĐÚNG HAY KO NHÉ BẠN
\(1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}.1\frac{1}{24}...1\frac{1}{360}\)
\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{24}...\frac{361}{360}\)
\(=\frac{2^2}{3}.\frac{3^2}{8}.\frac{4^2}{15}.\frac{5^2}{24}...\frac{19^2}{360}\)
\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}.\frac{5.5}{4.6}...\frac{19.19}{18.20}\)
\(=\left(\frac{2.3.4.5...19}{1.2.3.4...18}\right).\left(\frac{2.3.4.5...19}{3.4.5.6...20}\right)\)
\(=19.\frac{1}{10}\)
\(=\frac{19}{10}\)
\(1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}.1\frac{1}{24}...1\frac{1}{360}\)
\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{24}...\frac{361}{360}\)
\(=\frac{2^2.3^2.4^2.5^2...19^2}{1.3.2.4.3.5.4.6...18.20}\)
\(=\frac{2.3.4.5...19}{1.2.3.4...18}.\frac{2.3.4.5...19}{3.4.5.6...20}\)
\(=19.\frac{2}{20}\)
=1,9