Calculating Finite Sum in SQL?

Question

I'm trying to figure out a way in which to calculate the following in SQL:

Where r and W is static (0.2 , 0.4) respectively. The x resembles age, and does never exceed 68.

My Database has columns for x, r and W, where x is different for each observation.

My initial thought was a while loop, but i'm not able to construct a while loop, that does something like :

select * , 0 as n

while n < 68 - (x + 1)
begin
    (POWER((1 + r) / (1 + W)) , n)
    set n = n + 1
end

from data

Hopefully the pseudo-code above illustrates what i am trying to implement.

Thanks in advance!

Answer 1

There is no need for a loop. Your sum (given r,w,x) is

(POWER( (1+r)/(1+w), 68-x)-1)/( (1+r)/(1+w) - 1)

unless

(1+r)/(1+w) == 1

in which case the sum is 68-x

For if we write

c = (1+r)/(1+w) and 
N = 68-x

then

(c-1)*Sum{ 0<=n<N | pow(c,n)}
= c*Sum{ 0<=n<N | pow(c,n)} - Sum{ 0<=n<N | pow(c,n)}
= Sum{ 0<=n<N | pow( c, n+1)} - Sum{ 0<=n<N | pow(c,n)}
= Sum{ 1<=n<=N | pow( c, n)} - Sum{ 0<=n<N | pow(c,n)}
= pow( C, N) - 1 (as all the other terms cancel)