factorials and binomials simplification - nusum less verbose



Hallo.

I would like to simplify expression involving binomial coefficients and factorials. 

binomial(n+1,k) / binomial(n,k)      ------->       (n+1) / (n+1-k)
(n+1)! / n!        -------->        n+1

How can I tell the Maxima Simplifier to do that?

I'm using Maxima within the theorem prover Hol Light, through an interface written by John Harrison.
There is a Maxima command that is particularly useful for me, nusum, that makes hypergeometric sequences telescopic (if it's possible).
In order to parse its output from inside Hol, I need to make this command less verbose. Do you know how can I do?

Example
(%i1) display2d:false;
(%o1) false
(%i2) a(k):=1/2^(n+1) * binomial(n,k) * (2*k-n-1) / (n+1-k);
(%o2) a(k):=1/2^(n+1)*binomial(n,k)*(2*k-n-1)/(n+1-k)
(%i3) nusum(a(k), k, 0, k);
Dependent equations eliminated:  (1)
(%o3) -(k+1)*binomial(n,k+1)/(2*(n-k)*2^n)

I'd like to avoid the string "Dependent equations eliminated:  (1)".

Thank you.

Giovanni Gherdovich