a) $2020.2020-2022.2018$

$ = 2020^2-(2020+2).(2020-2)$

$ = 2020^2 - (2020^2-2^2)$

$ = 4$

b) \(\left(\dfrac{1}{4}-1\right)\left(\dfrac{1}{9}-1\right)\left(\dfrac{1}{16}-1\right)...\left(\dfrac{1}{400}-1\right)\)

\(=\left(\dfrac{1}{2^2}-1\right)\left(\dfrac{1}{3^2}-1\right)\left(\dfrac{1}{4^2}-1\right)...\left(\dfrac{1}{20^2}-1\right)\)

\(=\dfrac{\left(-1\right)\cdot3\cdot\left(-2\right)\cdot4\cdot\left(-3\right)\cdot5\cdot\cdot\cdot\left(-19\right)\cdot21}{2^2\cdot3^2\cdot4^2\cdot\cdot\cdot20^2}\)

\(=-\dfrac{1}{20}\cdot\dfrac{21}{2}=-\dfrac{21}{40}\)

Giải:

a) 

b) =(1/2²−1)(1/3²−1)(1/4²−1)...(1/20²-1)

=−1/20⋅21/2

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!!!!!!!

Tính :(1/2^2-1)×(1/3^2-1)×(1^4^2)×.....×(1/200^2-1)

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

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

\(=\frac{1.3}{2.2}\cdot\frac{2.4}{3.3}\cdot\frac{3.5}{4.4}\cdot\cdot\cdot\cdot\frac{19.21}{20.20}\)

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

\(=\frac{1.21}{20.2}=\frac{21}{40}\)

Dễ thấy \(\frac{21}{40}>\frac{-1}{2}\)

Vậy A > -1/2

Nhầm rồi :v, làm lại

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

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

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

\(=\frac{\left(1.2....19\right).\left[-\left(3.4.5...21\right)\right]}{\left(2.3....20\right)\left(2.3....20\right)}\)

\(=\frac{1.\left(-21\right)}{20.2}=\frac{-21}{40}\)

Dễ thấy \(\frac{21}{40}>\frac{20}{40}\Rightarrow\frac{-21}{40}< \frac{-20}{40}=\frac{-1}{2}\)

Vậy A < -1/2

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

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

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

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

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

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

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

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