So sánh à bạn?

A=\(\frac{1}{2}\).\(\frac{2}{3}\)....\(\frac{2012}{2013}\)=\(\frac{1}{2013}\)

B=\(\frac{2012}{2012.2013}\)=\(\frac{1}{2013}\)

vậy A=B

\(A=\frac{1.2}{2.2}.\frac{2.3}{3.3}.\frac{3.4}{4.4}.\frac{4.5}{5.5}.....\frac{2012.2013}{2013.2013}=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}....\frac{2012}{2013}=\frac{1.2.3.4.5....2012}{2.3.4.5....2013}=\frac{1}{2013}\)

\(B=\frac{2012.2013-2012.2012}{2012.2011+2012.2}=\frac{2012.\left(2013-2012\right)}{2012.\left(2011+2\right)}=\frac{2012}{2012.2013}=\frac{1}{2013}\)

\(\Rightarrow A=B\)

99.101 mới đúg nhé

=\(\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}.....\frac{10000}{99.101}\)

=\(\frac{2^2.3^2.4^2......100^2}{\left(1.2.3.....99\right).\left(3.4.5.....101\right)}=\frac{\left(2.3.4....100\right).\left(2.3.4....100\right)}{\left(1.2.3....99\right).\left(3.4.5......101\right)}\)

=\(\frac{100.2}{1.101}=\frac{200}{101}\)

\(\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{50^2}{49.51}=\frac{\left(1.2.3.4...50\right)^2}{1.2.3.4...50.51}=\frac{1.2.3...50}{51}=\frac{50!}{51}\)

\(\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\frac{4^2}{3\cdot5}\cdot\cdot\cdot\frac{50^2}{49\cdot51}\)

\(=\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\frac{4^2}{3\cdot5}\cdot\frac{5^2}{4\cdot6}\cdot\frac{7^2}{5\cdot7}\cdot\cdot\cdot\frac{50^2}{49\cdot51}\)

\(=\frac{2}{1}\cdot\frac{50}{51}=\frac{100}{51}\)

\(A=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{50^2}{49.51}\)

\(=\frac{2^2.3^2.4^2...49^2.50^2}{1.3.2.4.3.5...48.50.49.51}\)

\(=\frac{2.50}{1}=100\)

\(B=\frac{2.2}{1.3}.\frac{3.3}{2.4}...\frac{2015.2015}{2014.2016}\)

\(B=\frac{2.3...2015}{1.2...2014}.\frac{2.3...2015}{3.4...2016}\)

\(B=2015.\frac{1}{1008}\)

\(B=\frac{2015}{1008}\)