ok here it is..

Each spring obeys Hooke's law

So F_i = k_ix_i.

We get two more equations from the way the springs are connected. First, the tension is the same in all the springs:

So F_i = F

Second, the individual displacements of all the springs add to give the total displacement:

x_total = x_i

To solve the problem we write the additive term x_i as a function of the constant tension F.

x_i = F / k_i

and sum over all the springs to find the total displacement

x_total = x_i = F / k_i =  (1/k_i) . F ________(1)

And  F = k_eq.x_total 

=> x_total = (1/k_eq).F ________(2)

Comparing (1) and (2) ...

1/k_eq =  (1/k_i).