2nd last line on page 12... I am not convince with above statement. I used time line to understand. What i think is as.... Lhs is probability that life aged x survives x+ n. It doesn't give information about the surviving beyond x + n, then in Rhs why it is sum of surviving for each possible year and dying in next year? Can anyone explained in words?
RHS of the equation say x must die eventually in time n to infinity. So all we can tell is x must at least survive n years first before he can surely die in those time period.