\(\Rightarrow\)C=\(\frac{\text{1.2.3.4...99.100}}{\text{2.4.6....100}}\)
\(\Rightarrow\)C=\(\frac{\text{1.2.3...99.100}}{(2.2....2)(1.2.3.4.5....50)}\) [50 chữ số 2]
\(\Rightarrow\)C=\(\frac{51}{2}.\frac{52}{2}...\frac{100}{2}\)=D
vậy C=D
Mk thấy khó hiểu , bn có thể chỉ kĩ hơn đc ko.
#)Giải :
Ta có :
\(D=\frac{51}{2}.\frac{52}{2}.\frac{53}{2}.....\frac{100}{2}\)
\(D=\frac{51.52.53.....100}{2^{50}}\)
\(D=\frac{\left(51.52.53.....100\right)\left(1.2.3.....50\right)}{2^{50}\left(1.2.3.....50\right)}\)
\(D=\frac{1.2.3.....100}{\left(2.1\right)\left(2.2\right)\left(2.3\right).....\left(2.50\right)}\)
\(D=\frac{\left(1.3.5.....99\right)\left(2.4.6.....100\right)}{2.4.6.....100}\)
\(D=1.3.5.....99=C\)
\(\Rightarrow C=D\)
#~Will~be~Pens~#
\(D=\frac{51}{2}.\frac{52}{2}.\frac{53}{2}...\frac{100}{2}\)
\(\Rightarrow D=\frac{51.52.53...100}{2^{50}}\)
\(\Rightarrow D=\frac{\left(51.52.53...100\right)\left(1.2.3...50\right)}{2^{50}\left(1.2.3...50\right)}\)
\(\Rightarrow D=\frac{1.2.3.4.5.6...100}{2.4.6.8...100}\)
\(\Rightarrow D=\frac{\left(2.4.6...100\right)\left(1.3.5...99\right)}{2.4.6.8...100}\)
\(\Rightarrow D=1.3.5...99=C\)
Vậy C = D
\(D=\frac{51}{2}\cdot\frac{52}{2}\cdot\frac{53}{2}\cdot\cdot\cdot\frac{100}{2}\)
\(D=\frac{51\cdot52\cdot53\cdot\cdot\cdot100}{2^{50}}\)
\(D=\frac{\left(51\cdot52\cdot53\cdot\cdot\cdot100\right)\left(1\cdot2\cdot3\cdot\cdot\cdot50\right)}{2^{50}\left(1\cdot2\cdot3\cdot\cdot\cdot50\right)}\)
\(D=\frac{1\cdot2\cdot3\cdot\cdot\cdot100}{\left(2\cdot1\right)\left(2\cdot2\right)\left(2\cdot3\right)\cdot\cdot\cdot\left(2\cdot50\right)}\)
\(D=\frac{\left(1\cdot3\cdot5\cdot\cdot\cdot\cdot99\right)\left(2\cdot4\cdot6\cdot\cdot\cdot100\right)}{2\cdot4\cdot6\cdot\cdot\cdot100}\)
\(D=1\cdot3\cdot5\cdot\cdot\cdot99\)
\(\Rightarrow\text{ }C=D\)
