operation with sum



Hello all,

1) Is it possible to transform:

sum(x[i]+y[i],i,1,n) to sum(x[i],i,1,n) + sum(y[i],i,1,n)

2) In the following sequence:

(%i1) x[i]+y[i]=0$
(%o1) 0 = x[i] + y[i]
(%i2) sum(rhs(%o1),i,1,n)
(%o2)  sigma_symbol rhs(0 = x[i] + y[i])

How to force evaluation of rhs?
I have tried:
sum(''rhs(%o1)......
Or
sum(ev(rhs(%o1)........
But I give always sigma_symbol rhs(0 = x[i] + y[i])

Thank you for your help.