Question

\(choB=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right)....\left(\frac{1}{100^2}-1\right)\)

so sanh B voi \(-\frac{1}{2}\)

Answer 1

\(B=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right)...\left(\frac{1}{100^2}-1\right)\)

\(B=-\frac{3}{2^2}.\left(-\frac{8}{3^2}\right).\left(-\frac{15}{4^2}\right)...\left(-\frac{9999}{100^2}\right)\)

\(B=-\left(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{9999}{100^2}\right)\)(Vì có 99 thừa số, mỗi thừa số là âm nên kết quả là âm)

\(B=-\left(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{99.101}{100.100}\right)\)

\(B=-\left(\frac{1.2.3...99}{2.3.4...100}.\frac{3.4.5...101}{2.3.4...100}\right)\)

\(B=-\left(\frac{1}{100}.\frac{101}{2}\right)\)

\(B=-\frac{101}{200}< -\frac{100}{200}=-\frac{1}{2}\)

\(\Rightarrow B< -\frac{1}{2}\)

Answer 2

b với 1/2 hộ mình với