Question

Cho B=\(\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right).....\left(\frac{1}{100}-1\right)\)So sánh B với \(\frac{-11}{21}\)

Mong các bạn giúp mình nhé 

Answer 1

B = \(\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right)...\left(\frac{1}{100}-1\right)\)

B = \(\frac{-3}{4}.\frac{-8}{9}...\frac{-99}{100}\)

B = \(-\left(\frac{3}{4}.\frac{8}{9}...\frac{99}{100}\right)\)

B = \(-\left(\frac{1.3}{2.2}.\frac{2.4}{3.3}...\frac{9.11}{10.10}\right)\)

B = \(-\left(\frac{1.2...9}{2.3...10}.\frac{3.4...11}{2.3...10}\right)\)

B = \(-\left(\frac{1}{10}.\frac{11}{2}\right)\)

B = \(\frac{-11}{20}\)

Vì  \(\frac{11}{20}>\frac{11}{21}\)nên \(\frac{-11}{20}< \frac{-11}{21}\)

Vậy \(B< \frac{-11}{21}\)