Please help me further, I am unable to do
#Series of Binomial Coefficients
wet egret
dire osprey
Please help me further, I am unable to do
what did you do from 2nd line to 3rd line?
wet egret
I multilpied k to the numerator and denominator so that r! forms
dire osprey
I multilpied k to the numerator and denominator so that r! forms
what's with the n-k in the first term on 3rd line then?
wet egret
i opened the n-k+1 factorial
fast moon
the problem is that you have to analyze different situations. If n<50 then the summation will stop before k=50 and if n>50, then we are not covering all possible products. For instance, if you have n=10000000, then the result might not be a very nice closed form. Also, I suspect that you need three different formula for the final answer.
For n=50 this has a really nice closed form $$\binom{100}{51}$$ which can be proved by combinatorics.
heavy pikeBOT
Kevin S
