TOPIC - THE BINOMIAL THEOREM
- The Binomial Theorem $\displaystyle\large (x+y)^n=\sum^n_{k=0}{}^nC_k \,x^{n-k}\,y^k$
- Sum of the coefficients of $\large (x+y)^n$ is $\displaystyle\large\sum^n_{k=0}{}^nC_k =2^n$
Binomial Coefficients - properties
- $\large{}^nC_k=\displaystyle { n!\over k! (n-k)! }$
- $\large{}^nC_k={}^nC_{n-k}$
- $\large{}^{n}C_k={}^{n-1}C_{k-1}+{}^{n-1}C_{k}$
- $\large{n\choose k}$ means $\large{}^nC_k$
- $\large{}^nC_k=\displaystyle { n!\over k! (n-k)! }$
- $\large{}^nC_k={}^nC_{n-k}$
- $\large{}^{n}C_k={}^{n-1}C_{k-1}+{}^{n-1}C_{k}$
- $\large{n\choose k}$ means $\large{}^nC_k$
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