Question Number 122264 by mnjuly1970 last updated on 15/Nov/20
Commented by mr W last updated on 15/Nov/20
![(1+x)^n =Σ_(k=0) ^n (_k ^n )x^k (1−1)^n =Σ_(k=0) ^n (−1)^k (_k ^n )=0 lim_(n→∞) [Σ_(k=0) ^n (−1)^k (_k ^n )]=lim_(n→∞) 0=0](https://www.tinkutara.com/question/Q122265.png)
$$\left(\mathrm{1}+{x}\right)^{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left(_{{k}} ^{{n}} \right){x}^{{k}} \\ $$$$\left(\mathrm{1}−\mathrm{1}\right)^{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} \left(_{{k}} ^{{n}} \right)=\mathrm{0} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left[\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} \left(_{{k}} ^{{n}} \right)\right]=\underset{{n}\rightarrow\infty} {\mathrm{lim}0}=\mathrm{0} \\ $$
Commented by mnjuly1970 last updated on 15/Nov/20
$${thank}\:{you}\:{master}… \\ $$