Bài này dễ mà bạn cũng hỏi =(((

\(A=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)....\left(\frac{1}{400}-1\right)\)

\(\Leftrightarrow A=\frac{-3}{4}.\frac{-8}{9}.\frac{-15}{16}....\frac{-399}{400}\)

\(=\frac{1.\left(-3\right)}{2.2}.\frac{2.\left(-4\right)}{3.3}.\frac{3.\left(-5\right)}{4.4}....\frac{19.\left(-21\right)}{20.20}\)

\(=\frac{\left(1.2.3...19\right).\left(\left(-3\right).\left(-4\right).\left(-5\right)...\left(-21\right)\right)}{\left(2.3.4...20\right)\left(2.3.4...20\right)}=\frac{1}{20}.\frac{\left(-21\right)}{2}=\frac{-21}{40}\)

Dễ dàng nhận thấy \(\frac{21}{40}>\frac{1}{2}\Rightarrow\frac{-21}{40}< \frac{-1}{2}\)

Vậy \(A< -\frac{1}{2}\)

\(A=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)...\left(\frac{1}{400}-1\right)\)

\(A=\left(-\frac{3}{4}\right).\left(-\frac{8}{9}\right).\left(-\frac{15}{16}\right)...\left(-\frac{399}{400}\right)\)

\(A=\frac{-3.8.15...399}{4.9.16...400}\)

\(A=\frac{-3.2.4.3.5...21.19}{2^2.3^2.4^2...20^2}\)

\(A=\frac{-2.3.4...19}{2.3.4...20}.\frac{3.4.5...21}{2.3.4...20}\)

\(A=\frac{-1}{20}.\frac{21}{2}\)

\(A=\frac{-21}{40}< -\frac{1}{2}\)

vậy \(A< -\frac{1}{2}\)

thank you very much!!!!!!!

xét (1/4-1)*(1/9-1)*(1/16-1)*...*(1/400-1)

= \(-\frac{3}{4}\times\frac{-8}{9}\times-\frac{15}{16}\times.....\times-\frac{399}{400}\)

=\(-\frac{3}{2^2}\times\left(\frac{-8}{3^2}\right)\times\left(\frac{-15}{4^2}\right)\times........\times\left(\frac{-399}{20^2}\right)\)

dãy trên có số số  hạng là:( 20-2):1+1=19(số hạng)

mà các số đều là các số âm => có 19 số âm nhân vào nhau sẽ ra số âm

Vậy A< 1/2

tk mình nha bạn cũ

ok thank

Ta có  A=\(\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)....\left(\frac{1}{400}-1\right)\)

=\(\frac{-3}{2^2}.\frac{-8}{3^2}.\frac{-15}{4^2}...\frac{-399}{20^2}\)

=\(\frac{-\left(1.3\right)}{2.2}.\frac{-\left(2.4\right)}{3.3}.\frac{-\left(3.5\right)}{4.4}....\frac{-\left(19.21\right)}{20.20}\)

=\(-\left(\frac{1.2.3...19}{2.3.4...20}.\frac{3.4.5...21}{2.3.4...20}\right)\)

=\(-\left(\frac{1}{20}.\frac{21}{2}\right)=-\frac{21}{40}< -\frac{21}{42}=-\frac{1}{2}\)

câu hỏi tương tự trên OLM ấy, Cậu lên đó mà tìm nhé

Đây này, ai bảo k có hả?? Nhớ tick nhé

\(A=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)...\left(\frac{1}{400}-1\right)\)

\(-A=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{400}\right)\)

\(-A=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{399}{400}\)

\(-A=\frac{1\cdot3}{2\cdot2}\cdot\frac{2.4}{3.3}\cdot\frac{3.5}{4.4}\cdot...\cdot\frac{19.21}{20.20}\)

\(-A=\frac{1\cdot2\cdot3\cdot...\cdot19}{2\cdot3\cdot4\cdot...\cdot20}\cdot\frac{3\cdot4\cdot5\cdot...\cdot21}{2\cdot3\cdot4\cdot...\cdot20}\)

\(-A=\frac{1}{20}\cdot\frac{21}{2}=\frac{21}{40}>\frac{20}{40}=\frac{1}{2}\)

\(-A>\frac{1}{2}\Rightarrow A< \frac{1}{2}\)

lớp 8a3 nguyễn khuyến đúng ko