Question

b) (1- 1/ 2 ).(1- 1/ 3 ).(1- 1/ 4 ).(1- 1/5 )... (1 - 1/x) = 0,01 Giúp với ạ

Answer 1

b) ( 1- \(\dfrac{1}{2}\) ) . ( 1 - \(\dfrac{1}{3}\) ) . ( 1 - \(\dfrac{1}{4}\) ) ... ( 1 - \(\dfrac{1}{x}\) ) = 0,01

     \(\Rightarrow\) \(\dfrac{1}{2}\)    . \(\dfrac{2}{3}\)  . \(\dfrac{3}{4}\)  ... \(\dfrac{x-1}{x}\)  = 0,01

     \(\Rightarrow\) \(\dfrac{1.2.3...\left(x-1\right)}{2.3.4...x}\) = 0,01

     \(\Rightarrow\)  \(\dfrac{1}{x}\) = 0,01

     \(\Rightarrow\) \(\dfrac{1}{x}\) = \(\dfrac{1}{100}\)

     \(\Rightarrow\) x = 100

Vậy x =100

 

Answer 2

=>1/2*2/3*...*(x-1)/x=1/100

=>1/x=1/100

=>x=100