\(=\left(\dfrac{1}{100}-\dfrac{1}{1^2}\right)\left(\dfrac{1}{100}-\dfrac{1}{4}\right)\cdot...\cdot\left(\dfrac{1}{100}-\dfrac{1}{10^2}\right)\cdot...\cdot\left(\dfrac{1}{100}-\dfrac{1}{400}\right)\)

\(=\left(\dfrac{1}{100}-\dfrac{1}{100}\right)\cdot\left(\dfrac{1}{100}-1\right)\cdot...\cdot\left(\dfrac{1}{100}-\dfrac{1}{400}\right)\)

\(=0\cdot\left(\dfrac{1}{100}-1\right)\cdot...\cdot\left(\dfrac{1}{100}-\dfrac{1}{400}\right)=0\)

Ta có A là tích của 99 số âm ==>A là số âm

Ta lại có -A=(1-\(\frac{1}{2^2}\))(1-\(\frac{1}{3^2}\))......(1-\(\frac{1}{100^2}\))=\(\frac{3}{4}\).\(\frac{8}{9}\)......\(\frac{99.101}{100^2}\)=\(\frac{1.3}{2^2}\).\(\frac{2.4}{3^2}\)......\(\frac{99.101}{100^2}\)=\(\frac{1.2.3^2.4^2....99^2.100}{2^2.3^2.4^2.5^2.....100^2}\)=\(\frac{2.100}{2^2.100^2}\)=\(\frac{1}{200}\)==>A=\(\frac{-1}{200}\)>\(\frac{-1}{2}\)

A = (1/2² - 1).(1/3² - 1).(1/4² - 1)...(1/100² - 1)

A = -3/2² . (-8/3²) . (-15/4²) ... (-9999/100²)

A = -(3/2² . 8/3² . 15/4² ... 9999/100²) ( vì có 99 thừa số, mỗi thừa số là âm nên kết quả là âm)

A = -(1.3/2.2 . 2.4/3.3 . 3.5/4.4 ... 99.101/100.100)

A = -(1.2.3...99/2.3.4...100 . 3.4.5...101/2.3.4...100)

A = -(1/100 . 101/2)

A = -101/200 < -100/200 = -1/2

Vậy A < -1/2

Ta có: \(A=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right).....\left(\frac{1}{100^2}-1\right)< \)

               \(< \left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right)....\left(\frac{1}{100}-1\right)\)

                     \(=\left(\frac{-1}{2}\right).\left(\frac{-2}{3}\right).\left(\frac{-3}{4}\right)...\left(\frac{-99}{100}\right)=-\left(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{99}{100}\right)\)

                                                                                           \(=-\left(\frac{1.2.3...99}{2.3.4...100}\right)=\frac{-1}{100}\)

Mà \(\frac{1}{100}< \frac{1}{2}\Rightarrow\frac{-1}{100}>\frac{-1}{2}\) ( vì số âm nên ngược lại số dương)

Nên A > -1/2

CHÚC BẠN HỌC TỐT

\(A=\left[\dfrac{1}{100}-1^2\right].\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right].\left[\dfrac{1}{100}-\left(\dfrac{1}{3}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)\(=\left[\dfrac{1}{100}-1^2\right].\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right].\left[\dfrac{1}{100}-\left(\dfrac{1}{3}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{10}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)Mà \(\dfrac{1}{100}-\left(\dfrac{1}{10}\right)^2=\dfrac{1}{100}-\dfrac{1}{100}=0\)

\(\Rightarrow A=0\)

\(\left(\dfrac{1}{100}-1^2\right)\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)

\(=\left(\dfrac{1}{100}-1^2\right)\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{10}\right)^2\right]...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)

\(=\left(\dfrac{1}{100}-1^2\right)\left[\dfrac{1}{100}-\left(\dfrac{1}{2}\right)^2\right]...0...\left[\dfrac{1}{100}-\left(\dfrac{1}{20}\right)^2\right]\)

\(=0\)

Vậy...

Mình mới học lớp 5

mình ko trả lời được đâu nha!

A = (\(\dfrac{1}{100}\) - 1²).(\(\dfrac{1}{100}\) - \(\dfrac{1}{2^2}\)).(\(\dfrac{1}{100}\) - \(\dfrac{1}{3^2}\))...(\(\dfrac{1}{100}\) - \(\dfrac{1}{20^2}\))

A = (\(\dfrac{1}{10^2}\) - 1²).(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{2^2}\)).(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{3^2}\))..(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{10^2}\))....(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{20^2}\))

A = (\(\dfrac{1}{10^2}\) - 1²).(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{2^2}\)).(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{3^2}\))...0.(\(\dfrac{1}{10^2}\) - \(\dfrac{1}{20^2}\))

A = 0