So yn+1= (a/k) * yn = (a/k) 2 * yn-1= ... = (a/k) (n+1) * y1,

That is yn+1/y1= (a/k) (n+1).

Because y=k/x, x*y=k, that is, x1* y1= x2 * y2 = ... = xn * yn = k.

Because An=Xn*Yn+ 1

A 1*A2*A3*...* an = (x1* y2) * (x2 * y3) * (x3 * y4) * ... * (xn * yn+1).

= y 1 * x 1 *(Y2 * X2)*(Y3 * X3)*...*(Yn*Xn)*Yn+ 1/Y 1

=k*k*k*...*k*Yn+ 1/Y 1

=k^n*Yn+ 1/Y 1

=k^n*(a/k)^(n+ 1)

=k^n*a^(n+ 1)/k^(n+ 1)

=a^(n+ 1)/k