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Q.
Notation form of $(a+b)^{n}$ is
Binomial Theorem
Solution:
The notation $\sum_{ k =0}^{ n }{ }^{ n } C _{ k } a ^{ n - k } b ^{ k }$ stands for
${ }^{ n } C _{0} a ^{ n } b ^{0}+{ }^{ n } C _{1} a ^{ n -1} b ^{1}+\ldots+{ }^{ n } C _{ r } a ^{ n - r } b ^{ r }+\ldots+{ }^{ n } C _{ n } a ^{ n - n } b ^{ n }$
where, $b^{0}=1=a^{n-n}$
Hence, the notation form of $(a+b)^{n}$ is
$(a+b)^{n}=\displaystyle\sum_{k=0}^{n}{ }^{n} C_{k} a^{n-k} b^{k}$