SYMBOL OF AN EXPRESSION SATISFYING INEQUALITIES

I would like to check if

2/(d + g + 2*r + 1) - 4 >=0

or not.

But I would like to know it when r,g,d satisfy

1. r+g-d>=0
2. nchoosek(r+2,2) >= 1+2*d-g
3. g-(r+1)*(r+g-d)-(nchoosek(r+2,2)-2*d+g)>=0

And moreover, the value I get here

answer = inputdlg('Enter the value of N in the formula',...
             'Sample', [1 50]);
N = str2num(answer{1,1});

I would also like to assume that

1. N=nchoosek(r+2,2) -2*d+g

Does anyone knows how can I see which sign has my expression

assuming these 4 things I have mentioned above?

Answer 1

[Walter Roberson]

No, that test is not always true under those conditions . nchoosek is not defined for negative or fractional inputs but the test you want obviously fails if you constrain to nonnegative integers so we must assume that your variables are over the reals rather than nonnegative integers .