Define $P_n$ as follows: $$P_n(a,b,c) = \frac {a^n}{(a-b)(a-c)}+\frac {b^n}{(b-a)(b-c)}+\frac {c^n}{(c-a)(c-b)}$$ with $n \in N$.
I know that $P_2(a,b,c)=1,$ and $ P_3(a,b,c)=a+b+c$.
How can I find $P_3, P_4, P_5$?
Define $P_n$ as follows: $$P_n(a,b,c) = \frac {a^n}{(a-b)(a-c)}+\frac {b^n}{(b-a)(b-c)}+\frac {c^n}{(c-a)(c-b)}$$ with $n \in N$.
I know that $P_2(a,b,c)=1,$ and $ P_3(a,b,c)=a+b+c$.
How can I find $P_3, P_4, P_5$?