Formula calculation

[user1]

Hi,

Can anyone help the calculation of Y below using SAS code?

Y=A*(B)^-1+ A*(B)^-2 + A*(B)^-3 + A*(B)^-4 +……+ A*(B)^-N

Thanks a lot!

[Astounding]

Within a DATA step, and assuming you have variables A, B, and N:

y=0;

do k=1 to n;

   y + a*b**(-k);

end;

If B is actually an expression rather than a variable, put it in parentheses:

y + a*(b)**(-k);

[PGStats]

Or this, which should be faster:

    u = 0;
    v = 1/b;
    do k = 1 to n;
        u = (1 + u) * v;
        end;
    y = a*u;

[user1]

Thanks for you both for providing the answer, much appreciated! PG Stats, since the power is negative, should the sas code be revised?

as  u = 0;
    v = 1/b;
    do k = -1 to -n; u = (1 + u) * v; end;
    y = a*u;

Thanks and regards.

[PGStats]

No. k is only a counter, not the exponent. The exponent comes from the number of multiplications by v (= 1/b, = b**-1), i.e. the negative exponent results from multiplying by a negative power of b.

[user1]

Thanks again, PG Stats!!

[user1]

Thanks! How about if N has one decimal place, e.g. 14.1?

[Astounding]

What is the first term in the equation if N has one decimal place?

[user1]

In the equation, everything is the same, only if N is not an integer, the example is below and I need to calculate for each record (Y₁........Y_N)

Y₁=A*(B)^-1+ A*(B)^-2 + A*(B)^-3 + A*(B)^-4 +……+ A*(B)^-10.2

Y₂=A*(B)^-1+ A*(B)^-2 + A*(B)^-3 + A*(B)^-4 +……+ A*(B)^-20.3

^…….

Y_N=A*(B)-1+ A*(B)-2 + A*(B)-3 + A*(B)-4 +……+ A*(B)^-N.5

[PGStats]

Not clear. What is the term before the last?

[user1]

Thanks very much, PG!

the term before the last is: A*(B)^-N+1

For example,

Y₁=A*(B)^-1+ A*(B)^-2 + A*(B)^-3 + A*(B)^-4 +……+ A*(B)^-9 +A*(B)^-10.2

When I run the above sas code, the decimal 0.2 from the last term is missing.

[user1]

sorry, it is not -N+1, it should be integer -N+1, for example if N is 10.2, then the term before the last one should be A*(B)^-9 , not 9.2.