Given two positive integers a and b, 
, we define the function 
as the sum of the reciprocals of the products of all combinations of 1 to a taken b at a time. In Matlab we say that: R = sum(1./prod(nchoosek(a,b)')). For example if 
and 
:
, we define the function as the sum of the reciprocals of the products of all combinations of 1 to a taken b at a time. In Matlab we say that: R = sum(1./prod(nchoosek(a,b)')). For example if and : >> R = sum(1./prod(nchoosek(1:5,3)'))
R =
0.7083
Given a positive integer x, we are asked to evaluate the following double summation:
For example for 
:
:
In which, in Matlab, evaluates to:
>> S = sum(arrayfun(@(i) sum(1./prod(nchoosek(1:3,i)')),2:2))+sum(arrayfun(@(i) sum(1./prod(nchoosek(1:4,i)')),2:3))+sum(arrayfun(@(i) sum(1./prod(nchoosek(1:5,i)')),2:4))
S =
5.5833
Please round-off S to the nearest whole number. Therefore, the final output for the above example is 
.
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