Question

Tính :

\(A=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)....\left(\frac{1}{196}-1\right)\)

Answer 1

\(A=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)...\left(\frac{1}{196}-1\right)\)

\(A=\frac{-3}{2.2}.\frac{-8}{3.3}.\frac{-15}{4.4}...\frac{-195}{14.14}\)

\(A=-\left(\frac{3}{2.2}.\frac{8}{3.3}.\frac{15}{4.4}...\frac{195}{14.14}\right)\) (có 13 thừa số, môi thừa số là âm nên kết quả là âm)

\(A=-\left(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{13.15}{14.14}\right)\)

\(A=-\left(\frac{1.2.3...13}{2.3.4...14}.\frac{3.4.5...15}{2.3.4...14}\right)\)

\(A=-\left(\frac{1}{14}.\frac{15}{2}\right)=\frac{-15}{28}\)