I'm going through the dense book Lawler and Coyle "Lectures on Contemporary Probability" and finding the problems to be very difficult.
THe one I'm stuck on:
Show for every s > -1 the limit: L= (lim n->infinity) n^-s (infinite product from j=1 to n of) (1+s/j) exists and is positive.
I know the general rule for infinite products would indicate we have a divergent inner product... yet the limit exists, so it is the n^-s term that is confusing me. Any help/hints would be great.
THe one I'm stuck on:
Show for every s > -1 the limit: L= (lim n->infinity) n^-s (infinite product from j=1 to n of) (1+s/j) exists and is positive.
I know the general rule for infinite products would indicate we have a divergent inner product... yet the limit exists, so it is the n^-s term that is confusing me. Any help/hints would be great.
