Question

[Nguyên Vũ :D]

Bài 2: Tính nhanh:

a) \(\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot\dfrac{24}{25}\cdot.....\cdot\dfrac{120}{121}\cdot\dfrac{143}{144}\)

b)\(\dfrac{5}{9}\cdot\dfrac{21}{25}\cdot\dfrac{45}{49}\cdot\dfrac{77}{81}\cdot.....\dfrac{357}{361}\cdot\dfrac{437}{441}\)

^{_{ai làm đúng mk dùng 3nick mk tick cho :))))}}

Answer 1

[๖ۣۜDũ๖ۣۜN๖ۣۜG]

a) \(A=\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}.\dfrac{24}{25}.....\dfrac{120}{121}.\dfrac{143}{144}\)

= \(\dfrac{1.3.2.4.3.5.4.6....10.12.11.13}{2^2.3^2.4^2.5^2...11^2.12^2}\)

= \(\dfrac{1.2.12.13}{2^2.12^2}=\dfrac{13}{2.12}=\dfrac{13}{24}\)

b) \(B=\dfrac{5}{9}.\dfrac{21}{25}.\dfrac{45}{49}.\dfrac{77}{81}....\dfrac{357}{361}.\dfrac{437}{441}\)

= \(\dfrac{1.5.3.7.5.9.7.11.....17.21.19.23}{3^2.5^2.7^2....19^2.21^2}=\dfrac{1.3.21.23}{3^2.21^2}\)

= \(\dfrac{23}{3.21}=\dfrac{23}{63}\)

Answer 2

[Bao Khanh Luu]