Question

Tính các tích sau:

A=3/4 . 8/9 .15/16 . ..... . 9999/10000

B=(1 - 1/4)(1 - 1/9). ..... . (1 - 1/10000) 

C=(1 + 1/1.3)(1 + 1/2.4)(1 + 1/3.15). ..... .(1 + 1/99.100)

Answer 1

A=\(\dfrac{3}{4}.\dfrac{8}{9}.....\dfrac{9999}{10000}\)

A=\(\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.....\dfrac{99.101}{100.100}\)

A=\(\dfrac{1.2.3.....99}{2.3.4.....100}.\dfrac{3.4.....101}{2.3.4.....100}\)

A=\(\dfrac{1}{100}.\dfrac{101}{2}\)

A=\(\dfrac{101}{200}\)

 

Answer 2

\(A=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}.....\dfrac{99.101}{100.100}\\ =\dfrac{1}{2}.\dfrac{101}{100}=\dfrac{101}{200}\)

\(B=\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)...\left(1-\dfrac{1}{10000}\right)\\ =\dfrac{3}{4}.\dfrac{8}{9}...\dfrac{9999}{10000}\)

(làm như câu a)