I could use help determining whether the following can be solved analytically.

I have an equation $\displaystyle $\sum_{s=c}^{Q}\frac{s-c+1}{s+1}{Q\choose s}p^{s}(1-p)^{Q-s}=\frac{a-b}{a-d}$$.

Notice this equation is the binomial probability distribution from c to Q (as opposed to going from 0 to Q), and it is multiplied by $\displaystyle $\frac{s-c+1}{s+1}$$.

I understand that $\displaystyle $\sum_{s=0}^{Q}s{Q\choose s}p^{s}(1-p)^{Q-s}$$ simplifies to $\displaystyle $pn$$. Can a similar simplification be made to the equation I've presented above? Any thoughts on how I might go about it?

Thank you for your help.

Josh