formulaBinomial Theorem and General TermThe statement is given for a,b∈Ra,b\in\mathbb{R}a,b∈R and n∈Nn\in\mathbb{N}n∈N.(a+b)n=nC0anb0+nC1an−1b1+nC2an−2b2+⋯+nCran−rbr+⋯+nCna0bn(a+b)^n={}^{n}C_0a^nb^0+{}^{n}C_1a^{n-1}b^1+{}^{n}C_2a^{n-2}b^2+\cdots+{}^{n}C_ra^{n-r}b^r+\cdots+{}^{n}C_na^0b^n(a+b)n=nC0anb0+nC1an−1b1+nC2an−2b2+⋯+nCran−rbr+⋯+nCna0bn(a+b)n=∑r=0nnCran−rbr(a+b)^n=\sum_{r=0}^{n}{}^{n}C_ra^{n-r}b^r(a+b)n=r=0∑nnCran−rbrTr+1=nCran−rbrT_{r+1}={}^{n}C_ra^{n-r}b^rTr+1=nCran−rbrVariables & Notationaaaconstant, endpoint, or first termbbbconstant or endpointnnnpositive integer or indexrrrindex or common ratio
