Question

Tìm x biết: \(\dfrac{1}{2}\) : (1+\(\dfrac{1}{2}\)) : (1+\(\dfrac{1}{3}\)) : ... : (1+\(\dfrac{1}{x}\)) = \(\dfrac{1}{101}\)

Answer 1

`1/2:(1+1/2):(1+1/3):...:(1+1/x)=1/101`

`<=>1/2:3/2:4/3:...:[x+1]/x=1/101`

`<=>1/2 . 2/3 . 3/4 . .... . x/[x+1]=1/101`

`<=>1/[x+1]=1/101`

`<=>x+1=101`

`<=>x=100`