Problem 57507. Easy Sequences 88: Double Summation of a Combinatorial Function

• Created by Ramon Villamangca

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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 :

>> 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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Solution Stats

60.0% Correct | 40.0% Incorrect

• 5 Solutions
• 2 Solvers

Last Solution submitted on Apr 29, 2025

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