\(1.3.5.7.9...59=\frac{\left(1.3.5...59\right).\left(2.4.6...60\right)}{2.4.6...60}=\frac{1.2.3...60}{2^{30}\left(1.2.3...30\right)}\)
\(=\frac{31.32.33...60}{2.2.2...2}=\frac{31}{2}\cdot\frac{32}{2}\cdot\frac{33}{2}...\frac{60}{2}\)
Vậy \(\frac{31}{2}\cdot\frac{32}{2}\cdot\frac{33}{2}...\frac{60}{2}=1.3.5...59\)(đpcm)
\(CMR:\frac{31}{2}\cdot\frac{32}{2}\cdot\frac{33}{2}\cdot...\cdot\frac{60}{2}=1\cdot3\cdot5\cdot...\cdot59\)
Chứng tỏ:
\(\frac{31}{2}.\frac{32}{2}.\frac{33}{2}.\frac{34}{2}....\frac{60}{2}=1.3.5....59\)
Chứng tỏ \(\frac{31}{2}.\frac{32}{2}...\frac{60}{2}=1.3.5...59\)
chứng tỏ: \(\frac{31}{2}.\frac{32}{2}.\frac{33}{2}......\frac{60}{2}=1.3.5......59\)
Chứng tỏ rằng \(\frac{31}{2}.\frac{32}{2}.\frac{33}{2}...\frac{60}{2}=1.3.5...59\)
Chứng tỏ rằng:
\(\frac{31}{2}.\frac{32}{2}.\frac{33}{2}...\frac{60}{2}=1.3.5...59\)
Chứng tỏ rằng
\(\frac{31}{2}.\frac{32}{2}.\frac{33}{2}...\frac{60}{2}=1.3.5...59\)
P=\(\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot\cdot\cdot\cdot\frac{399}{400}\)
Chứng tỏ rằng \(P< \frac{1}{20}\)
Bài 4 :
a) Tính giá trị của biểu thức :
\(A=\left(\frac{1\frac{11}{31}\cdot4\frac{3}{7}-\left(15-6\frac{1}{3}\cdot\frac{2}{19}\right)}{4\frac{5}{6}+\frac{1}{6}\left(12-5\frac{1}{3}\right)}\cdot\left(-1\frac{14}{93}\right)\right)\cdot\frac{31}{50}\)
b) Chứng tỏ rằng : \(B=1-\frac{1}{2^2}-\frac{1}{3^2}-\frac{1}{3^2}-...-\frac{1}{2004^2}>\frac{1}{2004}\)