Question Number 2843 by prakash jain last updated on 28/Nov/15
![Prove by mathematical induction n(n+1)(n+2)...(n+r−1) is divible by r! n,r∈N.](https://www.tinkutara.com/question/Q2843.png)
$$\mathrm{Prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$${n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)…\left({n}+{r}−\mathrm{1}\right)\:\mathrm{is}\:\mathrm{divible}\:\mathrm{by}\:{r}! \\ $$$$ \\ $$$${n},{r}\in\mathbb{N}. \\ $$
Commented by 123456 last updated on 28/Nov/15
![N={0,1,2,...} or N={1,2,3,...} ???](https://www.tinkutara.com/question/Q2844.png)
$$\mathbb{N}=\left\{\mathrm{0},\mathrm{1},\mathrm{2},…\right\} \\ $$$$\mathrm{or} \\ $$$$\mathbb{N}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},…\right\} \\ $$$$??? \\ $$
Commented by prakash jain last updated on 28/Nov/15
![N={1,2,3,...}](https://www.tinkutara.com/question/Q2846.png)
$$\mathbb{N}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},…\right\} \\ $$