the prooff of the above has not been given in study module but that reasoning i have posted in the message below.
The proof of this relationship has not been give in the study material, this works on the ground that say if your annuity is payable per month so you take per month interest rate by taking V^(m/12) , V^(2m/12) and so on and your per month probability of survival is tpx^(m/12) , tpx^(2m/12) and so on so that is how the series comes to be (1/m) * (1+ V^(1/12)*tpx^(1/12) + V^(2/12)*tpx^(2/12) + V^(3/12)*tpx^(3/12)+ ......... V^(n*12-1)/12*tpx^(n*12-1))
