Sage refuses to evaluate summations...

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There are two ways to get the value you want.

One is to define a Python function rather than a symbolic function.

Define p and q:

p, q = 33, 21

Define the function:

def g(x):
    return sum(frac(j*p/q) for j in range(x+1))

Use it:

sage: g(10)
31/7

The other way, with g defined as in the question (after declaring j as a symbolic variable) is to factor the result.

sage: j = SR.var('j')
sage: g(x) = sum(frac(j*p/q), j, 0, x)
sage: g(10).factor()
31/7