: I need help evaluating the following sum:
:
:
: I tried writing a C++ program to help evaluate it, but because the
: factorials & exponents get so large the standard libraries cannot
: handle it nor any calculator I have. So I was hoping to get some
: advice on here. What would you recommend doing in order to solve
: this problem?
:
: (I am in the process of getting MATLAB, never used it, and if there
: is no simpler solution I was planning on learning to use it to
: perhaps help solve it.)
:
: Thanks...
:
Don't try to calculate 365! or (367-n)! or (1/365)^n; those individual values grow to fast outside the range of nearly all standard libraries.
Instead use maths to reduce those values. Write the first couple of n out. This will give you the following (I've left out the n*(n-1) for readability):
For n = 2:
365!/(365!) * (1/365)^2 = 1 * (1/365)^2
For n = 3:
365!/(364!) * (1/365)^3 = 365 * (1/365)^3 = (365 / 365) * (1/365)^2
For n = 4:
365!/(363!) * (1/365)^4 = 364*365 * (1/365)^4 =
(364 / 365) * (365 / 365) * (1/365)^2
For n = 5:
365!/(362!) * (1/365)^5 = 363*364*365 * (1/365)^5 =
(363 / 365) * (364 / 365) * (365 / 365) * (1/365)^2
As you can see the calculation can be reduced to a loop, which calculates (367-i)/365 and multiplies the results together. Finally the result of this loop can be multiplied by (1/365)^2 and n*(n-1). The result of each of these multiplication doesn't get very small or very large. The result may be quite small, but should be within limits of a standard library.
