So I want to find the sum of this expression:

1 +(2 /3)+(2/3)*(4/5)+(2/3)*(4/5)*(6/7)+...+((2/3)*(4/5)...*38/39)

without using any loops only with vector calculations.

So my general approach is to create the sequence: z=1, 2/3 , 4/5 ...38/39

x=c(1,seq(2,38,2)) ; y=c(1,seq(3,39,2)) ; z=x/y

So I have my sequence z but now i want to create the original expresion meaning that each current term of z is the term multiplied with all each previous terms.To do that i wrote:

n=length(z) ; i=2:n

z[i]=z[i]*z[i-1]

but it doesn't work.Any ideas of how to approach this?