Thread: Limit of sum of factorials/beta functions

Hi people.
I am faced with the following limit:
$$
lim_{k \rightarrow \infty} \left( \sum_{j=2}^k \frac{{k+a-j-1 \choose {k-j}}}{B(j+b,c)} \right)
$$
where a \in N, (b,c) \in R^2 constants, and B(j+b,c) the standard beta function. Of course the choose function can be expressed as a beta as well.
Can anybody help?
Thanks in advance.

Originally Posted by ory

Hi people.
I am faced with the following limit:

where constants, and B(j+b,c) the standard beta function. Of course the choose function can be expressed as a beta as well.
Can anybody help?
Thanks in advance.

Now we can read it.