So sánh M và N, biết

\(M=\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot...\cdot\frac{99}{100}\)và \(N=\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{6}{7}\cdot...\cdot\frac{100}{101}\)

cho A=\(\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot\cdot\cdot\frac{99}{100}\)

CHỨNG MINH \(\frac{1}{15}< a< \frac{1}{10}\)

CHO A = \(\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot\cdot\cdot\frac{99}{100}\)

CHỨNG MINH \(\frac{1}{15}< A< \frac{1}{10}\)

Cho M=\(\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot....\cdot\frac{99}{100}\)

       N=\(\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{6}{7}\cdot......\cdot\frac{100}{101}\)

a, Tính M\(\times\)N

b, CM M<\(\frac{1}{10}\)

Cho A = \(\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot...\cdot\frac{99}{100}\)

Chứng minh rằng \(\frac{1}{15}< A< \frac{1}{10}\)

tính:

A=\(\frac{1^2}{1\cdot2}\cdot\frac{2^2}{2\cdot3}\cdot\frac{3^2}{3\cdot4}\cdot\frac{4^2}{4\cdot5}...\frac{8^2}{8\cdot9}\cdot\frac{9^2}{9\cdot10}\)

B=\(\frac{2^2}{3}\cdot\frac{^{3^2}}{8}\cdot\frac{4^2}{15}\cdot\frac{6^2}{35}\cdot\frac{7^2}{48}\cdot\frac{8^2}{63}\cdot\frac{9^2}{80}\)

Cho \(A=\frac{1\cdot3\cdot5\cdot...\cdot995\cdot997}{4\cdot6\cdot8\cdot...\cdot998\cdot1000};B=\frac{2\cdot4\cdot6\cdot...\cdot996\cdot998}{5\cdot7\cdot9\cdot...\cdot999\cdot1001}\)So sánh A và B

G=\(\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\frac{4^2}{3\cdot5}\cdot\cdot\cdot\cdot\frac{50^2}{49.51}\)

H=\(\left(1-\frac{1}{7}\right)\cdot\left(1-\frac{2}{7}\right)\cdot\left(1-\frac{3}{7}\right)\cdot\cdot\cdot\cdot\cdot\left(1-\frac{10}{7}\right)\)

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