通項公式: C_m^n=frac{m!}{n!(m-n)!} (mgeq n)
(1)遞推公式: C_m^n=C_{m-1}^n+C_{m-1}^{n-1}
(2) C_m^n=C_m^{m-n}
(3) C_{m+r+1}^r=sumlimits_{i=0}^{r}{C_{m+i}^i}
(4) C_m^ncdot C_n^r=C_m^r cdot C_{m-r}^{n-r}
(5) ncdot C_m^n=mcdot C_{m-1}^{n-1}
(6)二項式定理: sumlimits_{i=0}^mC_m^icdot x^i=(x+1)^m Rightarrowsumlimits_{i=0}^mC_m^i=2^m
(7) sumlimits_{i=0}^m(-1)^iC_m^i=0
(8) C_m^0+C_m^2+C_m^4+cdots=C_m^1+C_m^3+C_m^5+cdots=2^{m-1}
(9) C_{m+n}^r=sumlimits_{i=0}^rC_m^iC_n^{r-i}
(10) sumlimits_{i=1}^nC_n^icdot i=sumlimits_{i=0}^nC_n^icdot i=ncdot 2^{n-1}
(11) sumlimits_{i=1}^nC_n^icdot i^2=sumlimits_{i=0}^nC_n^icdot i^2=n(n+1)cdot 2^{n-2}
(12) sumlimits_{i=0}^n(C_n^i)^2=C_{2n}^n
如果你不註意防范,患上類風濕性關節炎的風險就會增加。傢裡衣物總是晾不幹,被子濕漉漉的,地板和墻面滿是水跡,空氣中還有...